Should I store things in corpses?

No. Your items will not be safe, eventually, he will despawn.

*Although some dead bodies,either having been killed by you or in game event sometimes stick around for a while you can NOT count on this for safe storage. the answer is NO you cannot count on this for safe storage. some bodies that remain in game dead will be looted at random as well, had this happen to myself once when i did what your asking about.

hope this helped

According to this Respawn and DeadBody Timers mod on SkyrimNexus:

Vanilla Respawn Timer details

Npcs, Creatures and Items... respawn after 10 Days or 240 Hours..

Areas that are marked cleared on your map respawn after 30 days or 720 hours

Merchants Respawn Items every 24 hours..No Change..

Dead Bodies Remove themselves after X amount of Day

and If More than 15 Dead Bodies are in cell then Remover Features kick in

So, no. It is not safe to store anything in corpses.

I've read that named NPCs do not respawn in Skyrim. So Alvor won't come back (ie. it won't be reset). I wouldn't bet on his corpse staying there forever though.