I'll give my two cents on how to raise one without wyvern milk, as it can be difficult for newer players.

ASE: If you don't have the means to kill an alpha or knock out a female for milk, use Daeodons. Make sure their inventory is filled with cooked meat. Once the baby starts losing health from starvation, use Daeodon's healing to keep it alive. I recommend making a cryopod as well, since the baby may ask for milk as an imprint, and this can help reset its need to something else. You can also cryopod it to make more cooked meat for the Daeodon if it runs out and just release it back later. This will not hurt the Wyvern or ruin the imprinting process, just freezes it. Snow Owls are also useful, though if you have a high level one for this then you're probably at a stage where you can at least safely trap a female wyvern anyways.

ASA: Bison milk. Yeah, it's very simple and much easier. Get some bison milk (have a female bison nearby a non-adult for her to passively produce it) before stealing an egg and then it can be used as a replacement for Wyvern milk. No need for Daeodons unless bison aren't on your map and/or you don't have any milk to transfer. In that case then it's back to Daeodons or Snow Owls.

Good luck, and enjoy these beautiful beasts!

-HydroRex