I have a couple guns that have a high gloss finish.
One is a Weatherby MarkV Deluxe Lazermark the other is a Ljutic Trap gun.

There are no issues with either stock, I just want to clean and polish them. I don't want to do any sort of re-finishing.

What is a good product for a safe cleaning and polish?

Just a guess but what about Renaissance Wax? Or a lemon oil based product like Pledge?

Birchwood Casey gun stock wax.

Ren wax. I understand it's often used for museum pieces.

I agree with the Renaissance wax, I use it on all of my handguns, and my trap guns.

Rennaissance wax

Thanks for the advice. I will try the Renaissance wax.
I contacted Weatherby and they suggested Pledge wipes for just after use and a furniture wax for a shine.I was disappointed with there suggestions.
I like the Renaissance wax instead.

Long ago, 1959+-, I polished on this stock to be presented to Dodger owner O'malley. It was at the stock makers shop before the checkering was cut. There was a paste wax he said spread it and rub it with a cloth a lot.

OMG, I wish I had not seen that picture!

I’ve had very good results with Scratch-X and micro fiber cloth, followed up by paste wax.

For stocks with the “Remington type” heavy gloss finish this takes out scratches and scuffs to make it look like new.

https://meguiarsdirect.com/pro...scratchx-g10307-7-oz

Looks over at the collection of polishing compounds for the vehicles…huh, never thought of using that on a wood stock.
I’ve got everything from “oh so delicate” to fast cutting rubbing compounds.