I can not do the snot rocket either. On two of my bikes I keep a a small snot rag in a pouch on the top of my top tube by the head tube. On my old road bike I keep it in a small frame bag that straps in where the top tube meets the seat tube.

I also started wearing cheap cotton work gloves from the dollar store. I cut the fingers off for warm weather, and buy big stretchy ones to go over my cold weather gloves. This turns every glove into a full nose wiper.

I am sorry, canklecat, that you have the opposite problem. I suffer your symptoms when I don't ride, and that is one of the motivations for me to bike commute to work.