Is there a feasible solution to adding a front hand brake to a coaster brake equipped bike that has no brazings for a brake on the fork?

Most forks are drilled in the crown and will accept a caliper brake. If your fork isn't drilled, but is 20mm or 3/4" from the bottom to the crown race, you can drill it yourself. Just be careful to drill squarely.

Before doing so, measure vertically from where the hole will be (or is) to the rim and make sure you can find a caliper with appropriate caliper.

There is a drilled hole in the crowns center, but my LBS told me that it's for a fender & wouldn't work with any brake he knows of. Does this make any sense? It is to be, by the way, for a Fuji Saratoga crank forward cruiser, if that makes any difference.

Does not make sense, unless the reach is really, really long. Drum brake is always an option, have to re-lace the wheel.

You have the bike there. Measure the hole to rim distance and then see if you can find a caliper brake of comparable reach. If a brake exists that's reach, then it's only a matter of working out mounting it. The brake needs roughly 3/4" of usable surface at the front of the crown with a 6mm through hole in the middle. If the crown is tall enough, you might have to modify the hole, or maybe drill it through to the back, but these are only details to be worked through.

Consider fitting a wheel with a drum brake hub.
particularly if there is a need for a really long reach around a fat tire..

you can redo the rear too, with a 2 or 3 speed, and still have a coaster brake.

Thanks to everyone for their suggestions. Happily, the problem was solved earlier today with a trip to a different local bike shop that specializes in repairs but also carries Fuji. After a couple of false starts, he came up with a Tektro caliper in his spare parts box that works well enough for this particular bike's expected local errand low speed duties.