If you buy crypto currencies in one country and then travel to another country, as long as I have the passphrase and private key on paper, hidden in mulptiple places and the crypto on an online exchange, no kyc, p2p bought, non custodial and bought on a clean laptop, can I delete the website from by laptop, including the online wallet, and then sign in again to that exchange after travelling.
You are mixing many things up, paper wallets have nothing to do with exchange accounts that usually need your email address and password, but you don't have any control of coins in your account.
Access to your exchange account should be possible from anywhere in the world if you have your login details unless some country is in some restricted region, but they can always lock your account and freeze your coins or withdrawals like we see happening in Binance and other exchanges.
So my question to the highlighted part is, Say when you register for an exchange like Binance and maybe other you pick a location during and when you travel as in this OPs case, will you have to change your location in the exchange registration too for you to be able to transact or that wouldn't be necessary even if you have all your login credentials?