Take another look at the original sentence:
You wanted to fix it this way:
A comma splice occurs when you connect two main clauses with a comma alone. Ryan is highly allergic to cats is one main clause. He requires at least twenty god-bless-yous is the second main clause. Just because you add in the prepositional phrase as a result doesn't alter the fact that you have two main clauses connected with just a comma.
You might want to consult the rules for fixing comma splices and fused sentences.