I avoid stains on my handles. I don't know what it is exactly, but stains tend to really polymerize on the surface and give me a surface that is too smooth and causes heat/blisters. To me the difference is very significant. I prefer thin coats of BLO because it really soaks in and leaves you with a surface that still feels like wood in your hands. It is much easier on your hands that way and doesn't get slippery with some sweat. I have found that water based dyes give me much more satisfactory results. You might try some leather dye like Fiebings Leather Stain. It comes in many colors, can be cut, and if you check the MSDS spec sheet - you'll see that the ingredients are pretty harmless.
After a water based dye, I will follow up with BLO or another of my favorite oils (tung, walnut, beeswax) and your hands will never know the difference.