Don, bleaching wood is a very involved and difficult process. First, you have to remove all the finish. Since your cabinets are being built for you, see if you can find out what kind of finish they are using. There are finishes available to pros called conversion finishes that are very difficult to remove. You cannot apply a finish that is anywhere near as durable. If your cabinets are being finished with a conversion finish, quite simply I would not try to strip and refinish. If they are being finished with a polyurethane, refinishing is somewhat easier but it still will be a difficult job.
After you strip, you will have to bleach the old stain. Some stains respond to household bleach and others respond to oxalic acid. Other modern stains do not respond well to either and you have to use a 2 step system to get the color out. See if your cabinetmaker will tell you what kind of stain he used and I will check what little is available on this. Chances are that you will have to test to see what works.
After all that, you will have to do some light sanding since you raised the grain with the bleach products. Then you will have to restain and finally apply a new finish. You can apply the finish with a brush but it will not look as good as if it was sprayed. You should apply about 3 coats of finish with intermediate sandings.
It is possible to do this but do you have a good shop area with good ventilation? Without knowing how many cabinets you have, you are probably talking about working on them every night for 3 or 4 weeks or more. You can do this but it will take a major commitment. I would be happy to tell you how but this does get involved and we can take it a step at a time. Let us know.