You don't get the same exposure from working in a shop soldering all day than from the occasional hobby project. And if you have a simple fan, you are already doing more than most hobbyists.

Safety is not priceless. Regulators carefully calculate how much impact various safety equipment and practices have relative to their cost. And you too should consider how much you need it. Solder for hours a day, get the best fume extractor you can find, do a hobby project every other month, you can go cheap.

Anyways, I wonder if a simple small desk fan fitted with a surgical mask you probably have too much of would be a good compromise of simple, cheap, and better than nothing for hobbyists.

I have never bothered, personally, even when I built more of my own prototypes myself. Hobbyists should consider their personal risk and go in increments. If you are not in a situation where setting up monitoring for exposure to flux per the NIOSH handbook is appropriate, you probably don't need much mitigation either. Putting solder assemblies at a level where flux smoke won't go up into your face is a good idea and practically free. A fan is a good idea, especially if you have one already.

If you're fixated on getting yourself a fume extractor... well, to each their own.