IMHO, your best bet is just to talk with him and maintain an open honest & trusting relationship. For someone with such limited technical knowledge to try and snoop is just disaster waiting to happen. 1 of 2 things is GARUNTEED to happen....
1. You will find what you suspect, and it will cause major issues with the relationship... not pleasent to go through.
2. You will find NOTHING, meaning, either he is faithful & trusting, or he knows how to not get caught.
Snooping on his laptop is likely going to be painful or make you feel guilty depending on what is found, and i would have to advise against doing it. But it is your call after all. I just wanted to caution you before you get too far in.