I think either will work for what you want to do and at the ranges you plan to shoot. Neither would be my 1st choice for deer, but I understand that in this case you're using what you can find.
I ran the numbers through a calculator and the TTSX 140 is still at 1999 fps at 300 yards if you're getting 2600 at the muzzle. Most of what I read says 2000 fps at impact is needed for expansion. Load data says you should be able to get 2800-2900 fps with 140's though.
https://www.barnesbullets.com/wp-con...mingtonV10.pdf
But if accuracy is equal I'd choose the 162 gr bullet. They expand more than most, but 162 gr is heavy for 7mm caliber and I think it'll be fine. If hunting much larger game where you need lots of penetration and possibly have to take shots at less than ideal angles then the better penetration of the TTSX might be the better choice.