If you're not connected to shore power and you're not running the generator then there isn't any power coming into the transfer switch and it will be safe to open up and work on. But before you go there you might try a little diagnosis.
The transfer switch is normally set up to default to shore power. If you're getting power into the RV when connected to shore power then this side of the transfer switch is operating OK. If things aren't working then it's either the contacts are dirty or the mechanical springs aren't holding them closed.
Disconnect shore power and start the generator. After power stabilizes (about 30 seconds) the transfer switch, when operating, will connect generator power into the RV. If that doesn't happen then the transfer switch may be the problem - assuming your generator is working correctly.
Now disconnect shore power, turn off the generator and open up the transfer switch. The most likely cause is the contacts have gotten dirty or pitted. Clean then up with some emory paper and see if that solves the problem. Otherwise it could be the electronic control board that has gone bad. You might be able to find a replacement board, but the simplest thing is probably just replacing the transfer switch.