You can't be sure with that. Even the most reputable ones can have some bad days and you'll never know how bad and terrible the situation they can get in.
Just remember FTX, Binance has got hacked with huge funds and recall all of those big names in the industry in the past.
FTX went down a year after the heights of 2021. The vast majority of hacks don't happen at major exchanges, and if they do, it'll impact a very small portion of their accounts. It's all about statistics and probabilities. I'm more concerned about these exchanges locking your account than getting hacked (as another user pointed out).
The possibility is there on locking their user's account if you don't have much documentation on your funds. So, not just with the additional identity they are going to ask but also likely the source of funds and where it came from. If you can't provide any other documents from it and you'll just reason out as another holding of yours, it is up to them to decide to lock your account but they'll for sure going to release your money and won't let you use them again.