If you have the original type spoke rims. You have little choice but to use a tube (and a rim strip).
You can safely use a tube in a tubeless tire. But, you must assume the tire loses one step in speed rating.
If your shop doesn't know this, I'd seriously consider finding another shop, as another finesse point on mounting a tubeless tire on a tubeless rim is wrestling the bead into proper seated position about the circumference on both sides.
It's automatic, no brainer, seating with a tubeless tire on tubeless rims. But, not so with a tube type rim. The risk of improper seating, translates to tread center wander during rotation. This can make the bike "wiggle" at certain speeds.
I would urge you not to simply accept only the tires they have stocked locally. But, wait for properly sized tires to come in on special order. Old bikes have special needs in certain areas. And, popular or "vanilla" tires for modern bikes aren't always the best fit.
Cheers,