Step 1: Print out 10,000 copies of your program.
Step 2: Take the printout to a recycling center and trade it for money.
Step 3: Go down to the office supply store and buy a handheld calculator.
All joking aside, the operative word here is "practical". A handheld calculator has lots of parts...plastic, metal, LED or LCD, circuit board, etc. It isn't really very "practical" to build one yourself, as they can be had cheaply at just about any store. The guts of the thing is the circuit board. You have to design the circuits to implement your logic (your "program", if you will), get it fabricated, then worry about the case, the buttons, the display, etc. If you wanted to try and wire one up yourself using an old-fashioned breadboard then the result wouldn't exactly be "handheld".
An alternative would be to write your program as an iPhone or Android application. That might be more "practical", and the result would definitely be "handheld". However, that opens up a whole 'nother can of worms. Such as, do you have the tools and expertise to code for those platforms? Does it require approval, or "jailbreaking" the target device? etc.
Constructing the thing as an exercise, or as a hobby it might be fun to try. Just throw out any idea of being "practical" and have a go at it.
I like the sound of step two, since I’ll be using the companies resources for this project, I could make the tiniest of profits.
Alternative is, if the programming works, is there a company that could convert this into a handheld calculator? I've learnt over the last decade that maths is becoming a skill not so widely used, there three types of people out there, the ones that can count and the ones that can’t.
I know that giving staff a normal calculator should be enough but common sense is just not so common anymore. I would like to calculate stock code by piece, answer would result how many boxes.
Your best bet would be to locate a company that actually manufactures calculators or printed circuit boards, and pose the question to them. My guess is you probably don't want to go to the big boys like Texas Instruments, Hewlett-Packard or American Micro Devices. They deal in bulk and it sounds like yours would be a pretty small production run. I suggest doing a google search on something like "custom calculator fabrication", "PCB Fab" or something like that.
There might be something in your area, or there might not be. However, wherever you get the work done, it will probably be pricey. Custom electronics aren't too uncommon, but the companies that commission them generally want to do larger production runs (see FedEx or UPS, or Corrigo for examples) so finding a company willing to do your tiny run might be tough.