If you already have your wallet backups in cold wallets, that is good, and it does not harm your Bitcoin wallets and Bitcoin funds if you have any extra cold storage wallet backups on any extra devices.

Make sure you do extra backups properly and don't take risk to make it unsafely and carelessly so that it can be accessed by the other people who can steal your bitcoins.

Creating a cold storage wallet in Electrum.
[LIST] Open source hardware wallets.
[GUIDE] How to buy a Hardware Wallet the right way.

That old computer can hit its lifespan and no longer be usable in the future like next several months, couple of years, but as said, it plays a role as an extra backup for you. So if it is broken, it does not harm your bitcoin fund as you already have other backups to use.