From a bit more Googling, there do seem to be commercial SR22 sims out there with the side yoke - might be worth contacting them to see if it's something that can be sourced independently, but I'd expect them to be expensive.
Best bet would still be to get a CH USB yoke, remove the yoke, chop off the left handle, move the hat to the left retaining only the top left button on the left handle, then remount the left handle to the unit somehow. There's a few on Ebay for £20-40 so it wouldn't be too expensive to give it a go.