You are right, I didn't know much about the stable coins, I just read about them once but didn't think of using/trading.
Stable coins fit my needs as their price would remain constant irrespective of the price of Bitcoin(my previous assumption for wrong).
I believe that most exchanges would allow me to trade, with some maximum threshold, without the need to fill out the KYC.
Yea stable coins should be your best bet if you want to trade in exchange without withdrawing. Exchanges do allow transactions with max thresholds without KYC, but if you're planning to hold everything in an exchange, what if you can't withdraw it someday? Like you'd surpass the threshold already, and any more would require you to KYC? You'd have no choice then cause your profits are in the said exchange. What I said is completely possible if you suddenly make a massive profit in buying and selling BTC.
Plus, you haven't really told us what country you're currently living in. This possibly limits the exchanges you may participate on, without the need for KYC that is. Exchanges don't really need bank accounts when registering, and even when trading it isn't needed.