Tissue covering and high-tech options
Just FYI, the primary US aeromodeling association (Academy of Model Aeronautics, www.modelaircraft.org) has a plentitude of resources and articles on stuff like this, several of which I've read in their magazine, Model Aviation. I'm certain our British partners have similar resources, but more info sources are always nice...
For ultralight covering on wee-tiny-and-feather-light planes, the modern thing is "microfilm," which appears to be a high-tech version of cling-wrap. Dunno what its low-temperature characteristics are (which is likely to be critical for any plastic-based covering), but it is an option.
Heavier-duty self-adhesive shrink-on coverings like MonoKote, Ultracote, and similar are likely to be too vigorous in the shrinking department for this lightweight structure, BUT it's worth checking them out as options, 'cause some are less shrinky than others. For radar reflectivity, aluminized Mylar (Space Blanket stuff) may be worth a thought, though attaching it taut and wrinkle-free would be a nightmare, as it doesn't heat-shrink. Very snazzy look, though.
All that being said, the classic tissue and dope solution may well prove to be the most practical solution.