Which exchange? It's the wrong mindset that our funds aren't SAFU with CeX. I have been using Bitget for a long time now and keeping my funds there cause I see they have the transparency and proper security arrangements to safeguard user's assets. They review their wallet from time to time and the valuation of their Reserve Fund in addition to the User Protection Fund which is another layer.
Never you store your coins in exchange market, when you know you are not selling your coins at the moment, because your coins are not safe there, and many people has loss their coins in exchange because they leave the coins for a long period of time.
Any wallet that you know that is safe for your coins, I will advise you to continue using it to store your coins, and it will make you to have peace of mind anywhere you are because your coins are not in the exchange market.
I believe you have seen or heard about electrum wallet before, you can also try to add it to your wallets to hodl your BTC because it hard for scammers to scam your BTC from the wallet.
Or OP could use a cold wallet that they called or physical wallet, I know there are a lot of that product in the market and so far those physical or cold wallet are safe, I dont want to mention any product because I dont promote them, But I think that is a good product to use, yes you will need to buy it but its just a small thing in order to protect and store your assets other than storing it in an exchange which is not a good idea because there's a posibilit that it would be co.primised and your assets could be stolen, so yeah I recommend cold wallets, but you need to keep it with care because it is physical so if you lose or broke it then there will be a problem, anyway everything has its disadvantage but I think its more efficient and convinient to use that in an exchange platform.