I do pretty much as Mike Campbell does it. Sanding during the refinish can slide over into the checkering w/o much of a concern,,you're going to re-cut it anyway. No need to over do it though.
Recutting I generally use a carbide single line tool for the first pass. I don't know if you can even find them anymore, but they are a real work and money saver if you do a lot of restoration work.
Re-cutting old work eats up regular tools very quickly as the dirt&grit in the old checkering grinds away the sharp edges of the tiny tools.
A few can be resharpened at least a time or two, but most like the file style are toast. I've got a carbide that's been working steady for 25yrs and just showing some dullness now. It still is my first choice to re-trace old work.
I then go over the work with a regular spacer to even things up and deepen it. This second step really makes the checkering look a lot nicer when the spacer is used.
Some old work w/odd spacing resists it but there are single line tools around w/an adj spacing bar too.
It all depends on how involved you want to get in the work and how many jobs you'll be doing.
I have to work w/magnification. But I'd suggest it for anyone.
I usually brush in a single coat of thinned finish. Then stain the checkering at that point if I need to,,and I usually do as I stain most all of the wood I work with. Some do,,some don't.
But if you stain the raw checkering, it'll drink up the stain at a rate quicker than you might expect and become a couple shades darker than you wanted. A light finish coat first,,or even two, will prevent that.
(Tooth)Brush just a wisp of black chalk dust or other black powdered substance into the checkering when it's just about dryed. I'm still using up a jar of old copier toner. Works fine.
It'll put that older, used and handled look into the checkering for you,,if that's what you're after.
There's no one correct way to do any of this stuff. It's what ends up working best for you. Try a few different things suggested by others or things you come up with on your own.
The final results will tell you when you've found the 'right' way.
