Hi Big Sam.......welcome to TFF.
Sounds like what you have is a Remington Model 11, which is a license-built version of the famous Browning A-5. Remington made approximately 300,000 of these from 1911 to 1948.
The higher grade Model 11s (Special, Tournament, Expert, and Premier) have some collector value.....but if yours is a "plain jane" shooter in average or slightly above average condition (70-80% condition) the value would range from $150 to $275 (depending on whether it has a plain, solid, or vented rib).
If you just want to keep it as a "shooter"......sure, go ahead and reblue it.
A "comfortable" old gun is like a comfortable pair of old sneakers......they may not look great, but they sure do fit well.