Seriously, though – don’t. Use tieraps, or procure … dunno what they’re called – patch cables? Short cables, specifically for pedal boards. Or make them yourself, but with a soldering iron and jacks that have a soldering connection.
You can thank us later.
Ok, so it’s not a simple cable with a jack on each end. 
Any chance of contacting the control pedal manufacturer to find out exactly what type of cable it is, then?
The problem is the cable is hard wired into the device. If it was as simple as purchasing appropriate patch cables, we wouldn’t be having this conversation and this thread would not even exist.
Since you don’t like the pedal connected to the cable you could return those pedals and go with a Boss FS-6 Dual Footswitch (not necessarily the boss brand, there are plenty of options) that would allow you to use regular guitar cables.
Yeah, I’ve considered that. I may end up going that route
Fcuuuuuk.
The agreed-upon punishment for coming up with this arrangement is called the Testicle Removal Ritual. It proscribes sedation of any kind.
I think (for now), I’d leave it as it is… You may decide to do something different down the road with your setup… I too like all of my wiring neat and clean, but for now, focus on the usability of your setup… Just my opinion…
Good Luck!!
Never mind… I ordered the Boss device that @eric.kiser mentioned, which I should have done in the first place. This is the price I pay for trying to scrimp on the cost .
I have sent them several emails (they’re in China) with no response. I’m sending the pedals back and getting the Boss one that @eric.kiser mentioned.
I’m not terribly surprised at that, Pam 
That’s the spirit . . . 
This was a fun topic while it lasted, though 
Cheers, Joe
Yes, but like every other thread on this forum, it may help someone else down the road.
The coaxial cables you have worked with, I think, are both solid core coaxial cable. Guitar cables and the cables on your pedals are stranded core coaxial cable. The solid core are used for heavy duty or outdoor applications. The stranded core are usually for indoor applications where you need flexibility in your cables. There is more to it. I’m being brief to explain why the cables seem so different but the overall design is the same.
Splicing the cable is not recommended since it’s hard to get a reliable splice in these cables. The recommended way of doing this would be to cut it off to the length you want and put on a new instrument cable connector.
Edit: @PamPurrs You move quicker than I could type! 
The FS-6 is a nice (if expensive) utility pedal. It’s very versatile and the two pedals can be used for two different things if you ever decided you only needed one of the pedal functions for your SR-18.
There are polarity and mode switches on the back for each foot switch. If you have any problems getting it to work it will come down to having these switches in the right position.
The center connector (marked A&B) is for a TRS cable that lets you connect the two pedal switches with only one cable. It’s a nice feature, but the SR-18 doesn’t support it. You will still have to run two cables from the FS-6 to the SR-18.
Actually, I cancelled the order after I read more closely and discovered it requires a 9 volt battery and has no actual power supply. According to the reviews, if you don’t unplug it, the battery drains. I’ve had enough of that nonsense with the active bass I have.
I found a less expensive one that does use a power supply and ordered it.
WHAT? That sucks!
That takes a really cool pedal and turns it into something I will never recommend again. What a waste. I only messed with this pedal for a short while and I thought it was so great but I never got to the point of discovering this. Good thing you dug into it. They sure don’t make it obvious.
What did you end up going with?
This… I hope it works
https://www.amazon.com/gp/product/B07KQTFZRK/ref=ppx_od_dt_b_asin_title_s00?ie=UTF8&psc=1
I was looking at their information and based on what they say it won’t work.
The B connection would work. But the one that says A&B says it requires a TRS cable connection which the Alesis doesn’t support for the foot switches.
The thing about having a powered foot switch is the SR-18 doesn’t require that. Unless I’m confused and those HQRP pedals you have now are hiding batteries in them.
I’m still searching to see what else I can find.
LOL I cancelled that order also @eric.kiser.
At Amazon HQ I’m known as the Queen of cancellations and returns
The local UPS store has created a special entrance with my name on it.
No, they don’t.
Here’s what I’ve found out…
Alesis customer support have said in three different posts that “Any momentary, non-latching footswitch” will work.
I’m going to add to this that the switch has to be able to use a TS cable (regular instrument cable) and not a TRS cable (these have a second wire, like a stereo headphone cable).
I found three options that will work.
This one was designed for people that want to do exactly what you want to do. Specifically, it was made with the SR-16/SR-18 in mind. Drum Machine Footswitch $50
I don’t know anything about this company and I can’t make a recommendation one way or the other regarding this pedal. I think it’s interesting that since it exists at all, others have also wanted the same solution you’re looking for.
Next is this… Fender 1-Button Footswitch $35 each
I could swear I saw somewhere that this was a non-latching footswitch but I can’t find it now. I saw in one of your pictures that you have one. You could test it with the SR-18 and verify whether it works or not. I would sure like to know if you have a chance to test it.
The only downside is the connection is on the side which be cumbersome on your pedalboard if you decide to add things later.
Last is this… Boss FS-5U $40 each
These are designed to attach together and have the connection on the top edge. If money wasn’t a factor I would choose this one. But with the cost of cables we’re looking at $120 solution versus the $26 solution you have now.
As an alternative, if you want to minimize your cabling, you could do this…
Nux Dual Footswitch $40
To TRS cable $14
To TRS female to 2 TS male adapter $6
To the two connections on the SR-18
Based on the what Nux says, if you set the switch to ‘close’ then the switch will work non-powered and by using the TRS to TS adapter you get around the Alesis not accepting a TRS connection. Also, it would take up less space on your pedal board and reduce cabling. And after checking, it’s the least expensive solution I’ve brought up. This is what I would go with.
Good luck, Pam. Let me know if you have any questions.