AFAIK you should be able to do most of your cleaning with alcohol and compressed air. Its not normally difficult to get to the parts you need to clean if you remove the top cover. (Unplugged of course.) If you're getting a good image already and the video isn't having a bunch of audio dropouts you're probably ok for the time being. Most likely the cleaner tapes would work but I personally am always nervous to put a non-standard item into an old mechanical device that you may or may not ever find parts for again.
If you're wanting to keep this up, looking term its definitely worth seeking out the service manual for your vcr model if you can find it.
The other thing to make sure of is your capture settings. The deinterlacing algorithm can make a pretty significant difference.
After its captured there are a lot of AI "improvements" that can be made that will manufacture detail. Topaz AI for windows is kind of the gold standard at the moment but there's an open source project called video2x that might also work. Both would require a fairly decent gpu.
You are correct that this is technically in code and would protect against shock hazards in a neutral error situation but you also get the opportunity for the outlet to pop during the day when nobody is home and the battery to die.
We had a situation in our old house where someone who was technically correct but didn't think it through had a gfci outlet upstream of the refrigerator outlet. Thankfully it popped while someone was home and we got everything corrected before we lost everything in the fridge.