Reddit mentions of CNC Spoilboard Surfacing Router Bit 1/4’’ Shank Durable Carbide Tipped By SILIVN - 1 Pack (W10)

It really isn't. Just buy one of these things to open up the cart, pop the contacts off the old battery with a tiny screwdriver or something, slip on a new (obviously same-sized) one, then tape the contacts back on. I've done this for four different cartridges (Mario Land 2 and 3, and Pokemon Silver and Crystal) and I've never had a single problem. (As well, while you have the cartridges open you can (and probably should) also clean off the contact pins)

Deep clean your games.

To do this I would recommend a deep clean. These games have 25+ years of dust build up and corrosion from people blowing in them. And simply dusting it out might not be enough.

To deep clean the games you will need to open them up this can be accomplished with a 3.8 security bit screwdriver. You can get those here from amazon for a few bucks. After it’s opened gently remove the chip and wipe out the inside of the cart with some isopropyl alcohol to remove any dust inside and set it aside. Then move to the game contacts these are the gold slips at the bottom of the game. Dip a q-tip in the isopropyl alcohol and firmly scrub the contacts until the q-tip stops getting a dark color. Use as many q-tips as you need.

After that there should still be some alcohol on the contacts. Use a pencil eraser on the contacts and firmly rub off any hunk that might have built up. I found the pink rectangular ones work best.
Next take a magic eraser and buff out the last of anything remaining on the contacts. Do this to both sides and then take a paper towel and some alcohol and gently rub off any dust or eraser markings left behind. Let everything dry for a minute or so and the put the game back together.

If doing that doesn’t solve the issue it’s a problem with the 72 pin connector. Turn the NES upside down and use a Phillips head screw driver to remove the 6 screws on the bottom so you can lift the top off. After that remove the silver heat shield there are 2 screws on the left 2 at the back and 3 or 4 on the right side. Once that’s off blast the insides with compressed air to get all the dust out that has built up. After a good dusting remove the tray and 72 pin connector there are 3 screws on either side with the middle screw being longer then all the other screws. Side the tray foreword and up to remove them pull the 72 pin connector off the back.

You can bend the pins back up or boil it to clean it if you don’t want to buy a new one or really care about having all Nintendo parts ( if so let me know and I’ll explain how to do that as well), but I personally usually just replace it at this point. If you don’t really plan on using your NES very often you can get a basic 72 pin connector on amazon for $10.00. If you play it often you might look into upgrading to a Blinking Light Win it’s more expensive but it’s designed so you don’t push down on the game and loosen the pins so it should last much longer and it will circumvent the region lock chip. Personally I love mine.

I think that’s everything. Let me know if you need to know anything else. Good luck with the repairs