no real need for the paste.
A cooling pad is hit or miss, usually it just elevates the laptop while forcefully blowing more air into the intakes on the bottom (assuming the laptop has it's intakes on the bottom which it seems it does by what you've said about elevating it) and having all that air forcefully shoved through the system causes the fans to spin more than they should and wears them down, on top of the fact that typically these coolers doing such a thing also cause your laptop to get full of dust a lot quicker than it normally would which then decreases the performance of the cooling.
My suggestion is to just use something to elevate it slightly allowing for more air flow.
Something like these feet that will give it more elevation are worth it for the cheap price you'll pay.
Amazon.com: Practical Laptop Cooling pad Rubber Skidproof feet Heat Reduction Stand for Notebook/iPad/Laptop(pack of 4): Computers & Accessories
www.amazon.com
however, if you also plan on opening up the laptop and doing thermal paste, might as well also take that opportunity to clean out any dust buildup in the cooling system using compressed air that way, the new paste combined with cleaning the dust out and elevating it should hopefully yield a slight further decrease in temps than the 10c you get just by elevating it.
But also keep in mind that laptops generally run hotter than desktops because of the cooling being more limited and because of this they are designed to run hotter without issues but running 70c under load when elevated is actually really nice already so just simply elevating the PC using something like the feet I linked would do wonders.
You don't don't have to get those feet though and shop around for something you might like better than those.