I would put the old tube in one of the new size tires and inflate it enough to see if it will fold up or not
What size do you use now and what size do they recommend to use on the smaller tires.
I've seen a lot of regular old tubes in street tires(back in the 1960 and 1970s when I owrked in gas service stations that use to sell a lot of tires to their customers) that had folds in them due to the tech not inflating those tubes several times without the valve stems in them and letting them deflate several times 2 or more times to insure the tubes did not have folds in them before inflating them to the proper pressures for the tires
I haven't used tubes in a lot of years now, all my slicks get run without tubes in them even if M/T recommends using them