Green’s Dictionary of Slang

one who effects swaps or exchanges.

1680		E. Hickeringill Reflections on Late Libel etc. 28: The Author had [...] been Lecturer there at this day, (for he is no Starter, nor Shifter, nor Swapper of Livings) [OED].
1833		J. Neal Down-Easters I 101: I shouldn’t wonder if he was to try, added the swapper on my left.
1908		N.Y. Tribune 1 Nov. 6/1: That bunch of horse swappers and fortunet tellers [i.e. gypsies].