sram 10 speed parts are all interchangeable between road and mtb. shimano 10 speed mtb and road are not interchangeable either with each other or with sram. shimano and sram 10 speed cassettes are fully interchangeable with each other.
So if you have a 10 speed sram shifter, then any 10 speed sram rear mech should work, with either a shimano or sram 10 speed cassette. If you have shimano 10s shifters, you need a shimano 10s mech (either mtb or road, to match your shifters). sram 10s shifters are not compatible with 7/8/9 speed mechs.
Sram use 1:1 ratio, I'm not sure what shimano use now. But even if shimano used 1:1, the levers would still need to pull the same amount (number of mm per click) of cable as sram, to make them both compatible. If sram 1:1 pulls 4mm of cable per click and shimano 1:1 pulled 5mm, then they would both be 1:1 pull ratio, but would not be compatible (cable pulls are just a guess, I have no idea what the actual cable pull is on either of them for 10 speed)
So if you already have the shifters and the apex rear mech will cover your gear range, then it should work fine.
I think there are a lot of single left hand shifters available probably because they've sold all the right hand ones as singles for 1x drivetrains...
disclaimer: there are some tricks to make various combinations of sram and shimano 9 and 10 speed mechs and shifters compatible but I haven't tried them and can't comment. I imagine if you have plenty of time for messing about with spacers and trying different combinations then you can probably get something to work. but for the price of an apex rear mech, my guess is that would be a lot cheaper, take less time and messing about, and probably work better.