I own two Charter Arms Undercover 38s as well. One is from 1987, and I bought it the day I was sworn in as LE. The other is 21 years older, and was my dad's until he died in 2010.
Both are decent shooters (the newer one a little easier due to thicker, checkered stocks) and I trust them just fine.
Looks like you have reason to trust yours as well, in your hands, at least.