Possibly any sort of solvent that will evaporate completely. In addition to water: alcohol, MEK, white spirit/odorless mineral spirits, etc. If any of your pigments are soluble in your solvent, that's a no-go. And, as you said originally, you have to wait for the solvent to evaporate.
Only other option seems to be dry-blending. You might study some industrial blenders and emulate one on a tiny scale, especially tumble-blenders. The challenge there will be to get the mixed pigment out completely, leaving no residue to contaminate the next batch. Almost all of these machines have internal vanes to ensure complete mixing, leaving all sorts of surfaces and nooks & crannies that have to be cleaned.
Mini-sized clear plastic storage jars might work, as you could shake, turn, roll, etc. until you've achieved the blend you want. Cheap enough that you could reserve sets of them, one each for various color families around the color wheel, making contamination less of an issue.
By the way, I've been mixing colors for paint for 15 years now, and I don't find it easy... and linseed is used primarily for its refractive properties rather than its cheapness. The gem-like color of a well-formulated oil paint is inimitable owing to its apparent depth.