I have restored more air rifles than I care to remember, I wouldn’t bother reblueing, I have done this successfully with the Birchwood Casey reblue but to get it right you have to prepare the steel correctly, a good start to taking off any surface rust is use oil and 0000 fine grade wire wool, I have brought back some quite rough looking guns to a nice standard this way, if the steel is pitted then it is what it is!
Your gun, the infamous HW80.
Yours is a Mk2 full length going by the stock shape and barrel length, these guns are notorious for going over the legal 12ftlb power limit due to the size of the piston/chamber, they were not designed for the UK market, more the US market under the Beeman name rather than Weihrauch, it’s known as a magnum chamber as the capacity is a fair bit larger than say a HW77, they would easily shoot sweetly at 18ftlbs+, under 12ftlbs they can feel very lazy in comparison to a rifle that has a smaller piston, it may be worth getting your local gun shop to try it over a Chrono to check the power as you do not want to be caught with an over powered air rifle, your in section 1 firearms then without a license..
As has been said, any animal that is to be shot needs respect of being killed instantly with no pain, practice practice practice until you are confident in your gun and skills, seeing a creature in pain that has been caused by your own hands is no fun..
Here is what a bit of fine wire wool and oil can achieve -
Before, a 1970 Feinwerkbau 300 with surface rust.
After, just fine wire wool and oil plus I restored the stock.