I know you don't want to refinish, but it sounds like that's what they need. Do a few coats of the boiled linseed oil to put life into the grips, and then coat them with Arm-R Seal from General Finishes. Or you can use a number of other products. Arm-R Seal is just really, really easy to work with. Apply multiple coats with a nylon stocking, sanding very lightly between coats.
My reasoning: I build furniture, so I've done way too much research into finishes. That aside, oils dive into the wood, which is what makes it look so good. More coats of oil generally makes nicer looking wood products. I've used tung oil for a few projects, and it works awesome, but takes a long, long time to dry. Because it penetrates, it gives life to the wood, but doesn't offer a layer of protection on the surface, where it is most needed. So add some protection there. Arm-R Seal is very easy to work with and very tough. Another option would be to hit it with a spar urethane.
I'll stop ranting now. Oil will definitely bring life back to the grips, but I'd definitely consider a little extra protection on them.