What is the best way to apply Shellac-based primer?

Shellac/alcohol based primers like Bulls Eye work great for sealing stains and odors in many applications, however they do put out a lot of alcohol fumes. Spraying increases the amount of volatile gases in the air and should only be used in a very well ventilated area and with proper protective respirators. You can actually get very intoxicated, legally drunk from hours of exposure. There is always a risk of fire or explosion if a large concentration of alcohol fumes are exposed to an open flame or hot spark, so be very careful.

I have dealt with the identical problem of neutralizing smoking odors in an apartment. I believe you will have equal success using a good latex/water based primer. A water based primer is easier and safer to use, and I'm sure you will see good results. Because to the large areas you need to seal, I'd recommend avoiding shellac and go with latex.