However if it's big enough to be messing with orbits around neptune it's likely pretty large. If it's large then the hawkings radiation isn't going to be visible.
So if it's moon mass it's going to be 0.1mm and at 2.7 kelvin or so. Earth mass is 9mm, but even colder. Generally for the orbital changes they are seeing in a wide variety of objects it seems like the mass is even larger still.
Even seeing pluto is hard, even a jupyter mass black hole is only 3 meters or so. So no I don't think we could detect it via hawking radiation.
We might however see high energy particles resulting from the somewhat messy feeding that black holes are known for. If we sent a probe it could plausibly get close enough to directly observe hawkings radiation. Pretty amazing thought, maybe we will get that lucky.
Surely a "large nuclear bomb" isn't very strong when you're talking about things on black hole scale?
Ah, looks like I was "a bit" low. Wiki claims 5×10^6 megatons of TNT when it finally evaporates. Apparently about the energy the shoemaker level struck Jupiter.
