I'm about as far from a paladin as you can get, but he wouldn't be able to cast any of his magic without his connection to Tyr. One could mimic those spells, sure, but I don't know of a way he'd be able to do them without it.

[ aside from like fun undead magic, but obviously lay on hands isn't that. So weird!! How the fuck does an undead do that. Tyr, explain ]

It's best not to go pressing it too much--shake his faith and he might not be able to do it any longer.