Welcome to our forum.
At the base of the spa, below the cabinet, on the black wood trim just before the ABS plastic that the unit sits on, there is a small silver piece with your serial number, etc. You can use that info to get all the info on your spa. You can even call other dealers and see what the cost of the speaker is to them and see about shipping. This way you can see what the pricing is an how it stacks up.
Artesian Spas website has a database for dealers that when entered can give you a parts list of your tub. The only way your tub wont be on there is if it is too old. 2005 is how far back it goes, but 05-07 isnt the most reliable. If your tub is from 05 or new, the guy you're talking to is being lazy.
I need to clarify as I did this poorly: The dealer has the ability to look up parts based on the serial number of the tub. They have a special dealer log in and from there they can look up the parts for your type of unit. Don't let them tell you otherwise. Talk to a manager if you must.
If the stereo is still working why not unhook the speaker wires and pick up a couple of outdoor speakers and then splice in wire and run it to them? Those artesian speakers will only last so long then your out again and a waste of money.
They also make bluetooth decks that can throw to speakers. Check Crutchfield.I don't think I would invest anything in speakers for your tub. Save your money for something different.