USB Fume Extractor project combines a small craft box, 12v case fan, aquarium carbon filter, dc boost converter and some basic electronic components to create a USB powered fume extractor which treats your lungs to some clean air when soldering. Check the USB Fume Extractor video how the project works:
USB Fume Extractor was designed to from a USB port and not require batteries or a wall wart. Note that the assumption here is that quickly blowing the toxic air over a cheapo carbon filter made for water is going to significantly remove the toxins. I am not sure how well it does that, but I think that it will not remove all the toxins but that it would be still far better than nothing. Maybe a filter specifically made for the purpose would be better.
The basic idea for DIY soldering fume extractor is good. I have also made years ago my own soldering fume extractor based on idea from a commercial Fume Extractor. I tool a quite big mains powered fan (from old computer hardware) and used the same filters as a commercial unit used (just ordered them as spare parts). It has worked well for many years. I have not seen the mains powering to be disadvantage because also the soldering iron works with mains power (if you plan to build your own check also this diy fume extractor plan also). Here you can see a part of my fume extractor on the right and center: