I once made the mistake of sending the coins that I've freshly mixed to Bitstamp instead of the ones in my regular wallet from which I always deposit there,  quite a large sum, so above 10k, but I haven't had a problem with them nor was any delay or any further inquiry, I was already verified, the account is 5 or 6 years old so probably they don't even care anymore, this could obviously change if a new user with zero trades deposits 4BTC out of the blue. But probably the risks are there even if you're not mixing coins at all, Bitstamp at least has asked a lot of users about proof of funds, so, the path those coins have taken becomes irrelevant. 

As for instant exchanges, I would stay away since a lot of these cases happen ¹