Private investigators aren't always worth it.
I knew my husband was cheating and contacted a P.I.
He said, "Honey, you already know he's cheating. I'm not going to take your money."
California is a no fault divorce state meaning that adultery is neither here nor there. I could have spent tons of money on "proof", but I already had all the proof I needed. The lies, the people calling from work looking for him and him getting home super late from work telling me he had to work overtime and was with everyody from work having drinks afterwards.
Funny....they told me he was going to get fired if he didn't call and he didn't answer any of my 911 messages on his cell.
That said, "shady" behavior doesn't always mean he's having an affair.
Depending on what "shady" means.
Have you found another woman's earrings in the car? Do people call and hang up when you answer? Does your husband claim to have out of town business trips that his office doesn't even know anything about?
I think you should ask your husband about his shifty behavior, if that's all it is at this point, and see what he has to say before doing anything drastic.
Just my opinion.