Never had an induction cooktop. Why can't you use a wok? I can see why it wouldn't be as nice as having a flame, but are induction woks really so bad as to be unusable?
You can get woks with wider bases for induction cooktops. I haven't tried one, but I think it could fix the issue.
https://www.tefal.co.nz/c/Daily-Cook-Stainless-Steel-Non-sti...
1. For a round wok, you'd need an 'adapter' to hold the wok. 2. for a flat bottom wok, you might not get enough surface area on the induction element.