I'm a little worried about them toning down things a bit too much as well. While Uncharted might not be the best comparison as it's relatively not as violent, one of the weird things the Tomb Raider movie reboot did is that they took the 2013 reboot-which is pretty much TEMPLE OF DOOM on steroids-and made into a relatively 'safe' PG-13. They kept the same basic look of Lara from the game (although made her more sassy and Jolie-esque than the frequently PTSD suffering Survivor Lara) and the concept of a lost Queen/Island but that was pretty much it.
The first three games also had heavy supernatural elements but the Fourth game kind of ditched that (although the one in 3 was strongly implied to be some kind of hallucionagenic rather than anything mystical)
I'm guessing they'll probably ease up on Drake killing thousands of mercenaries which is a frequent joke about the games.
One thing I'm curious about is if the Scottish guy is actually Charlie Cutter, a double agent in the games.