DSA - maybe. RSA - what's wrong with that one given you have a 4096 bit key?
Yubikey currently supports 4096 bit RSA keys as a part of GPG applet. There's a PIV module, however in terms of elliptic curves it only has ec256 and ec384 and I still can't get ssh and pkcs11 to pick up anything other than built-in 2048 RSA keys.