Is it a 88-95 or a 96-99? 95 and older you can do it for a couple of bucks. 96 and newer will need to use a tuner to fix the speedo.
I did the same thing as you. Lifted with 35s and stock gears. Trans struggled a lot and I went thru 2 of them (under warrenty) and then finally regeared to help it out. If you are going to keep stock gears, drive like a grandma and put a trans temp gauge on it. IMO these 4L60s are not designed with a full size truck in mind. These transmission are better for a S series trucks and cars.
It's not the going fast part that gears are good for, they help reduce the amount your trans will have to shift and down shift. This will cause your trans to build up extra heat and in turn wear out parts faster.