(Spoilers All) Mance = Rhaegar Tinfoil Thought - The Shadowcat

I've been reading a lot of posts about this theory and admittedly have been drinking the kool-aid.

Most debunk the theory saying that GRRM confirmed that Rhaegar is dead and that he was cremated.

I apologize if someone already brought this up, but I haven't seen it in any online posts - this forum or otherwise.

Is it out of the realm of possibility that Rhaegar could have warged into an animal before his body died? The reason I ask is because the catalyst leading to Mance deserting the Night's Watch is after he gets attacked by a shadowcat while ranging. He is healed by a Wildling woman who patches his Night's Watch cloak with red silk.

Is it possible that Rhaegar overtook Mance's body?

In AGOT, when Arya is playing on the Trident with Mycah they find a shadowcat's lair. So shadowcats are known to live where Rhaegar died.

Not probable, but not impossible?