They can have dry skin. The Oilatum cream is ok, it’s as you say basically parafin. The tiny amount of Oilatum cream you’d be rubbing onto his ears won’t harm him if he ingests some.
To me it does sound like a possible mite-problem though, since the hair comes out easily. It’s very, very common for mite-tests to come up negative. You can treat empirically (=on suspicion) and Revolution (selamectin) is the best choice drug. A vet needs to prescribe it though. OTC anti-parasitics are most often not effective against mites. Advantix sometimes is, but it’s not as bunny safe as Revolution. Ivermectin works too. Whatever you use, be careful with dosage.
NEVER use any compound that has fipronil in it (Frontline, Sentry, Effipro and others). Fipronil is deadly toxic to rabbits. (I’m issuing this warning here, because we always do in discussions about antiparasitics for rabbits.)
I think you could try the Oilatum or other really fat cream first, and see if it resolves the problem. If it doesn’t, it’s probably time for mite-treatment.
Skin issues can also be food-related.