I've made a transaction today by unstaking my tokens so yes, you should be ok. I would create a paper wallet to send your EOS to (EOSindex have a good paper wallet tool for this - they are reputable) Then using your keys you can create a greymass wallet. This wallet seems to be the most popular solution at the moment, also recommended by Dan Larima https://eos.greymass.com
Be aware, you might only have 10 EOS available if you normally hold more than 10. This is because the rest are staked by default for all accounts and you have to unstake them to turn them into liquid. You might be ok from an exchange but I just thought I'd make you aware. I nearly had a heart attack when I only saw 10 tokens. lol
EDIT: If you have held your EOS in binance, it might be better to leave them for the time being as they will support some of the airdrops if you had your tokens during the snapshot. I read this on binance earlier today
I have to thank you for amazing answer