Is it safe to move ADA coins from one Ledger device to another while staking?

I currently have a small bag of ADA that I’m staking via a Nano X that is paired with Daedalus. I recently became aware that the paper sheet where I kept my 24 seed phrase has gone missing. At this point, I have no idea if I or someone in my household threw it away mistakenly. I’m not gonna wait around to find out, so I’ve ordered a new Nano S+, which I’ve already set up with LedgerLive and have successfully moved other coins I had in the Nano X over to the Nano S+. I know that in Cardano we dont give up custody when we stake, so in theory I should be able to move my coins without any issues. However, before moving forward, I wanted to post the question to the community just in case I’ve missed anything. Thanks in advance.