Are active charcoal air filters effective against finishing fumes?
I'm wondering if using such a filter will allow me to safely apply finishes in my basement workshop (brush or wipe, not spray)?
These are actually two very different questions.
The first is probably best answered no (some effect but without data to go on you can't rely on them). The second is obviously highly dependent on all the many variables.
The main variable is actually you, since individual responses to VOCs vary a great deal — some people can work around varnish all day without apparent ill effect, some people the spirit vapours makes them feel sick in a very short time. In addition there is the type of finish or finishes (so different solvents or solvent mixtures), the amount of ventilation in the basement (total air exchange) and last but not least, the length and frequency of exposure.
Assuming no protection, if an average person doesn't finish too frequently in their basement and for not too long a period each time in general they shouldn't have much to worry about from using varnish or shellac, but bear in mind that wiping varnish is much higher in spirits than regular varnish so the solvent vapours will be consequently higher (possibly double or triple).
Elsewhere in the house
Last thing to bear in mind is how the air from the basement vents into the rest of the house, since the basement obviously doesn't exist in isolation. If you have central air then there's a possibility that some significant portion of the VOCs will end up in other rooms, or all rooms, of the house.
Very low levels at low frequency are usually nothing to worry about, but again people's responses vary. Obviously any babies or children must be considered, ideally their exposures should be as close to zero as possible.
If you want to be completely safe when using finishes to protect yourself from VOCs then you should wear a respirator with the appropriate solvent-rated cartridge fitted. Note these can have a surprisingly small usage window once the seal is broken and continue to degrade even when you are not finishing, consequently some users store theirs in ziplock baggies between uses to protect them from air and extend their life.
If you want to work largely unprotected you should read up on some of the relevant numbers in MSDS safety documents, in particular PELs (Permitted Exposure Levels) and TWAs (Time-Weighted Averages). A starting point here.
There are some finishes to consider that have no VOCs and they would of course be the safest options. This would be principally BLO but also tung oil and walnut oil, as well as a soap finish.
Wax may seem to be no-VOC options but paste waxes are made soft with the addition of some spirits so they do give off a little solvent vapour, but it is very little and usually nothing to concern yourself with.