Shotguns are not hot blued. They are slow rust blued. It is a time consuming process that shows in the craftsmanship. It is only slightly more expensive than hot caustic bluing, which again, would be incorrect. Cold bluing is the least protective of all finishes, and usually ends up splotchy, if that's a word. Generally speaking, rust bluing for single barrel shotguns should run you $200 or less, plus polishing and prep time. This is what slow rust bluing looks like on a Winchester 20 gauge with nickel steel barrel, generally considered the hardest metal to achieve a quality finish on:
Here is a Winchester Model 1906:
And again, a Winchester Model 12 12 gauge:
Hot caustic bluing didn't come around until extreme mass production in the 50s, I believe. Just about everything prior was either rust blued or carbona blued. As far as wood finishing, there are a lot of techniques that can be used. I personally prefer to raise and sand to 400 grit. Then I apply varnish to fill in wood pores. Let dry for a minimum of 12 hours. I'll sand and repeat usually 6-8 times. Then I'll apply boiled linseed oil by hand. I'll again let dry a minimum of 12 hours, then sand with 0000 steel wool and repeat usually 6-10 times until the proper finish is completed. This is why gunsmiths charge the premiums we do. A true smith will put ALOT of time into properly restoring a firearm. It is craftsmanship.
Let me know if I can help restore your family heirlooms.