No, you just need a signature. But an Ed25519 signature, which current commercially available smartcards just cannot do.
You could be hacking something together with a Nitrokey or maybe Yubikey, those can do Ed25519 signatures. But generally, you would need to fiddle a lot with the implementation, because currently signatures are done in the kernel module, and you'd need to get that into the USB-device for signing and back again. Not impossible, but not implemented yet.
Another way would (theoretically) be to implement different signature algorithms for the wireguard key exchange, ideally some that common smartcards do support. But wireguards author left out cryptographic agility on purpose, so any work in that direction will be incompatible with the original implementation, or at least a very ugly kludge.
WireGuard does not use Ed25519. Indeed, it does not use any public-key signature algorithms at all. The long-lived static key (the peer's public key, their identity) is a Curve25519 ECDH key.
Of course, there are smartcards that could do this, you're just not allowed to have them. Plenty of smartcards nowadays are just flash and an ARM core which theoretically could be programmed arbitrarily. These tend to be used for credit cards, etc. Of course they might have acceleration units for specific algorithms like NIST ECDSA but I'd be surprised if Ed25519 couldn't be accommodated.
Unfortunately they're all NDAware, so they may as well not exist. ...But of course I've written about my extensive issues with the smartcard industry before.
You'll have to write some glue code, but if all you need is standard Ed25519 signatures, current-gen Yubikeys can do this. Somebody's implemented a python library that does that here https://github.com/tschudin/sc25519
You could be hacking something together with a Nitrokey or maybe Yubikey, those can do Ed25519 signatures. But generally, you would need to fiddle a lot with the implementation, because currently signatures are done in the kernel module, and you'd need to get that into the USB-device for signing and back again. Not impossible, but not implemented yet.
Another way would (theoretically) be to implement different signature algorithms for the wireguard key exchange, ideally some that common smartcards do support. But wireguards author left out cryptographic agility on purpose, so any work in that direction will be incompatible with the original implementation, or at least a very ugly kludge.