In industrial settings activated charcoal impregnated with sulfur compounds is used to trap mercury and prevent release into the atmosphere. The problem in a home setting using this approach is two-fold. First, there is no way to measure if the adsorbent material has reached capacity and is no longer functioning, and second, the used activated charcoal has to be disposed of as toxic waste. With some research you could probably decide on a time schedule for replacing your filters, but to be certain of zero release you would probably want to err on the conservative side and replace fairly frequently. There is some cost involved in that approach.
While the amount of fumes released during mercury development is sufficient to endanger the operator in a confined space (thus the use of fume hoods) released to the atmosphere it adds a negligible load to the existing mercury burden. Within moments it is at concentrations that would be difficult to even measure. Generally ensuring that your exhaust opening is at a sufficient height is an adequate safety precaution.
If it is very important to you to not even add minimally to environmental mercury loads, activated carbon filters impregnated with sulfur are available and would work. Some research would help you determine a replacement schedule and identify a location that would accept the resultant toxic waste for safe processing.
Per jgmotamedi’s post, these comments apply only to fume hoods that exhaust externally. I strongly discourage any home practitioner from using a recirculating fume hood for mercury development.