I will be changing the OEM 17" wheels and tires (245/70R17) on my 07 GMC Sierra to 18" wheels with (265/65R18) tires. The driver's door sticker on the Pickup say to to inflate to a Cold PSI of 35lbs. Should I just use the maximum PSI stamped on the new 265/65R18?

 

I haven't looked up if the 18" wheels are correct for your vehicle, several issues need be dealt with when doing this. But, we're talking about pressure anyway.

Assuming that the Tire Tread Width and the 18" Rim Width are the same (hopefully) you could easily adjust the pressure to Maximum Cold Inflation without any problems. In fact, all tires are built to run at their maximum recommended pressure for life. So, if your tires are cold rated at 55 lbs max, then putting 55 lbs in them, is NOT over pressuring them.

The recommended 35 psi (or any sticker number) is selected more for a reasonable load carrying capability, with the most comfortable ride (sort of a tradeoff). In my case, I never pay any attention to that, and (cold) inflate my tires, to about 10% under the recommended maximum, as stamped on the sidewall of the Tire.

Yea, that's a rougher ride, but...
My gas mileage is "better".
The control in cornering is MUCH better.
The front tires present a much better footprint when braking hard.
The rigidity of the sidewalls reduce flex, and don't heat up as much.

There are probably several other features about this, which others may choose to add, but, the most important one that I've noted, and IS the most important to me, is the control issue. I'll give up a lot, as long as when I turn that wheel, it'll go where I want it to, in an upright position.

 

Run it at the spec on the door. Factory equipped trucks with 17,18 and 20 still use 35

 

OR if using a reputable shop, the tpms' can be reprogrammed pretty easily. i do this a few times a week. without a hitch. never a complaint, or issue.