Disposable needles for 78 players are still made... you don't have to go to flee markets to buy them.
That aside its not really the best way to listen to 78's... I recently sent for a turntable from Esoteric Sound in the States... 6 fixed speeds + a variable.... and a diamond stylus.
The old players had very heavy arms .. not a good idea to keep using if you want to preserve your records. Apart from that many early "78's" were 80rpm and a number of other speeds depending on the maker.