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Bug wouldn't be too hard aside from Whitney, and poison? Pfft, don't bother. Poison is the worst type ever, ignore it.
If it helps, I did a poison type mono-run in firered. ( I know, not exactly the same, but still) And the team was actually pretty decent choosing the right pokemon. The team I used was: Nidoking, Tentacruel, Crobat, Venusaur, Muk, and Gengar.
I'm not sure how many of those are available in HGSS (well, Venusaur isn't main game, obviously) but all in all it was a rather decent team that could cover its weaknesses rather well.
I feel like bug would be horrible at covering its main weakness (Fire), so that sounds like the harder run to me if you're looking for the bigger challenge but -shrugs- who knows.