Udyr Shield should scale with Health only
I don't think his Shield that scales with AP makes sense at all and is not effective at all. AP Shield never was beneficial for Udyr. On other hand you do build health like Sunfire Cape, Titanic Hydra, Randuin, Deadman and many others that would benefit you
If you build Cinderhulk / Sunfire cape that would benefit both phoenix and Tiger at once
Phoenix does AoE damage so does Cinder and Sunfire For Tiger you can get Titanic Hydra which also scale with Health
So if you think about it "I build health because i want to get more tanky" makes way more sense than "I build Ability Power to get more tanky"
Poppy, Sion, Nautilus and so on get Health scaling on their shield and i think Udyr should get health shield too for the reasons i mentioned
On top of that Health Scaling Shield on Udyr would make him even more tanky if he runs Resolve / Tank Keystones - Courage, Grasp and Stoneborn