"New" means that you'll still have to shut of the supply valve... That means those channel locks... Here's where the problem can arise... That "supply line" will have to be removed in order to install the new one... I agree that going new is the way to go...

The entire job comes down to shutting off the supply valve... There is but so much torque you can put on the oval shaped handle of the supply valve... 90% of the time the channel locks will work... WD40 won't help... This is internal... It won't get there... It it takes more effort that lifting 10 pounds (with the channel locks) then you shouldn't go beyond that...

If that is the case then you will have to shut off the water and hope that the supply line nut itself isn't as bad... BTW, don't reuse the old supply hoses... Use new ones... They will most likely be 18" and labeled "Faucet" which means that the top side will have a large nut on it...

B~