patio door handle

I need a replacement sliding glass door handle that is keyed. It is a 3 15/16" and my door is 1 1/2" thick. I looked on your site and found a handle set part #82-035 but it is for a door that is 1 5/8" thick. Can I still use this handle with shorter screws or do you have a similar set that will work on a 1 1/2" thick door? I am going for an easy to grab and hold inside handle like the one I mentioned, but don't have a ton of money to spend.

Thank you!