Remind me at the next Whepstead White Horse session (I hope you're coming again!) - I can think of a few tunes that would do nicely.
Two that Mary and I have recorded as a set would work well - "The India War/ Jack's Health" (both Playford-ish though the first was actually written by Michael Raven.) You're welcome to use them! Maybe some French-style Scottisches Like Frederic Paris's "Ganivelle" and "Le Canal en Octobre" which also work as a set. Or the Abbotts Bromley Horn Dance Tune... Anyways what's wrong with morris tunes? Many of the Fieldtown ones are terrific.
These are all gentle dance tunes that steer a reasonable course between frenetic jigs and reels vs. weepy slow airs, if that's the kind of thing you are looking for.