Add keyed lock to patio door

I'm looking to add a keyed lock to my patio door. I believe that product 82-035 with 82-315 would be what I need. Only problem is that the handle (82-035) says that it is for a door 1 5/8" thick and my door is 1 1/2" thick. Would the screws that attach the exterior handle to the interior handle be too long for my door or would they work? If they would be too long, is there another handle set for my 1 1/2" thick door? Thank you! Nick

Sounds good, I wanted to make sure that I wasn't missing a different product that would eliminate the chance of dealing with the screws, but yeah, if it is a problem it shouldn't be hard to fix. Thank you!