Originally Posted by
revi
The main problem might be the minimal focusing distance of your lenses.
Not knowing how tame the animals are, the 40mm might put you too close to them for comfort (theirs, and yours). If you want to take a portrait of a gecko, your target is about 2 cm long, so you'll be working at 1/1 scale. A 40mm lens would put you at less than 8 cm from the gecko. For the same kind of shot with a 200mm, you would be at ~40 cm of your subject. But does your 55-200 focus close enough to get the shots you want? Perhaps test on a drawing or mock-up.
Then, I suppose with 'fixed lights' you mean continuous lighting? That might give off too much heat for comfort, esp. with the frogs, but the pets' owner should be able to tell you that.