"The cub". I've asked native speakers. According to them, "by default", pentu is a cub, it is not even very evident that it is a puppy (although it more likely to mean puppy than any other cub). So, in the absence of context it is either "the cub" or "the puppy". For "the kitten", "kissanpentu" is much better.
That's not a gerund because it's not functioning as a noun. Anyway, the reason why that's not accepted is because the verb that's being translated is "puraisee", not "puree". The former is temporally confined, expressing a single bite. The -aista/-äista suffix can be used with some verbs to create momentane verbs (the infinitive form of the verb is "puraista"). Momentane is a verb aspect in Finnish and Navajo that indicates that the action is brief.