I think in your case you're better off with a wheel-on trainer, like the Kick'r Snap. BUT it might have a 130mm minimum requirement for the QR, which you can fix with 4 mm of washers on each side.

With that, and a cadence sensor, and maybe a heart rate monitor, you'd be completely good to go on Zwift. Just make sure to cover the bike with towels or something for the sweat. I use a sweat guard which fits over the headset and most of the top tube, and a towel that covers the bar tape. The trainer sits on a yoga mat, and I put an old bath towel on top of that. And it's on a tile floor, because the sweat doesn't stay confined to the area directly under me. Oh! And get a couple box fans. You'll need 'em!