The pony shouldn't be saddle specific broke, however that being said if it's only been ridden with using a bareback pad, stirrups or irons may spook the pony because it's never felt them before. If the pony was ridden western, then saddlrseat or English would be fine, if the pony has only been ridden English or saddleseat then it may take a few longings before he gets used to the extra leather from a western saddle, but all saddles are similar in the fact there's a back pad, and a girth, westerns have a front cinch and a rear strap to help keep the saddle from ,flipping on a working roping saddle or even trail saddle when climbing or defending steep slopes.
Check with the current owner what type of saddle they have been using on him, if they have the fancy breed specific one then you may have to get him used to a different one.
I have found when working with horses that were broke and worked with one type saddle it just takes a few days of getting used to the new hardware before they settle down. Most of the quarter horses and appaloosas car in off the track, they were uneasy at first with an English saddler compared to racing seat, once they got used to English, we did English with western pads so they got used to them touching. Within two weeks we had western saddles on them and just let them walk around getting used to the feel, then lunging them a couple days and finally a rider. Riders felt familiar so it wasn't such a traumatic experience.