Hi Steve - physically, you should be fine. I have the normal Kickr, not the Core, but believe fitting wise these are fairly similar. I’d highly recommend a new cassette for trainer as its a pain in the **** changing cassettes.
From a spinning out perspective …you might get away with it depending on how fast you go in Zwift.
I just chucked your 44t chainring and a bigger one into online calc and comparing against my last Zwift sprint, if I had your gearing, I would spin out. But to give you perspective (as an upper Cat C rider), I could probably comfortably keep in the front group of most races as it would only be the sprint that I’d hit any limitations from cassette/chainring …from bikecalc.com
Workouts use ERG so you never change gear so you will be find with those rides, and on hills you can play with Trainer Difficulty to avoid spinning out descending, and some even resort to adjusting wheel size in the Wahoo app to help them solve this problem (a lot of people ask the question you are but with ~32t chainrings from their mtb’s).