It turns out that in addition to having all the high and low pass filtering I could ever need built in, Audacity will let me frequency shift the sound up and down! Neither the effects menu or the help files refer to this as "transposing," unhelpfully; the option is under "Change Pitch" near the top of the effects menu.
https://garagebandmeetupsingapore.wordpress.com/2010/04/25/using-audacity-to-transpose-tracks-change-pitch-without-changing-tempo/