I wouldn't recommend putting a UV in your tank itself, as it would likely damage your biological filtration.
If you don't have a sump, you could probably run some plumbing with a pump specifically for a UV sterilizer, other folks more handy than myself might have ideas on how to implement it, but I am sure it would be doable.
A sterilizer as I understand it, can aid with managing ich, killing off free swimmers. However I believe you are going the 'eradication' way, so likely also not necessary. Definitely couldn't hurt though, as I have heard it can also help combat nuisance algae.