Consider that tru-oil is brownish/amber, so get dye that is consistant with that - colors like purple or blue or green would be nada. Colors like red... maybe. Darker browns would be ok. On second thought... some greens might be ok too, sort of an olive type of thing.
The problem might be the interaction of the whole mess. You can get acetone based, mek based, alcohol based, water based, dry... .all sorts of dye. I think I'd go for an acetone or mek based dye, or mix dry pigments with acetone or mek or even better - white spirits (which are, as we have found out, greater than 53 percent of tru-oil).