What I have used on aircraft with wood or tube fuselage in the past is a cross of aluminium high speed tape with each leg the same length as the antenna, at the centre of the cross use a small piece of foil to ensure continuity between the two halves of the cross.
On the wood fuselage of the Chilton this is under the fabric of the turtledeck with a small clip to the underside to attach to the coax. In the metal tube fuselage of the Tiger and Auster the ends of the cross legs attach to the top longeron with a foil for continuity.
when the installations have been checked our avionics engineer reckoned the signal was at least as good as on a sheet metal structure with the antenna grounded to the structure.
If you want to learn about antennas in airplanes, read all the articles that Jim Weir wrote in Sport Aviation and Kitplanes. He is right on about antennas.
I have a 2 meter antenna on the rear of my hanger made from #12 copper house wiring and PVC pipe. Can pickup 6 repeaters up to 60 miles away. Installing a new 40& 80 meter ant behind hanger in the woods. Back in the early 60's, I used to make beam and ground plane antennas from metal clothline props and other junk for Ham and CB radios.
Back to the original posters aircraft, that is an aliminium "cage" structure, internal antennas are then no good idea. Some sort of whip is probably a better choice. The old WW2 fighter antenna strung from the cockpit to the tail fin do not work due to the pusher configuration of the plane.
Yes, it will work. Connect the coax braid to the metal structure, the center will go to the whip. The suggestions on the copper tape and the AL flashing as a counter poise (ground plane) are solid, good ideas. A free and clear counter poise and antenna is actually best from a noise standpoint, sometimes connecting to the frame actually increases RF noise (rf noise, alternator whine, strobe pulse generation, etc.). If the airplane is built and running, crank up a handheld unit nearby with the squelch set to 0 or minimum. If you hear lots of ignition noise, you may need some ferrites on the dc feeds to the strobes, the dc lead to the radio and on the alternator (on the alternator, most use a "choke" which can cut the typical alternator whine). For length, go to www.qsl.net, search for antenna calculations and several will pop up. A quarter wave antenna will be right at 2ft long...two wires 4 ft long, connected at the midpoint in the form of an X will also work as a counter poise, under fabric or Fiberglas. I personally would avoid putting the whip part (the radiator) under fabric...silver paint is AL and will affect performance. If you know a ham, borrow a VHF SWR meter, try the antenna, and as others have said, trim for the lowest SWR. It is like drag on an airframe, when it is clean, you get the best performance. I've built hundreds of antennas for many projects, I rarely have more than $5 in one. Use RG8 mini coax or RG 58, either will work well at air and frequencies. Crimped connectors are strongly suggested, as it ain't easy fixing one in an airplane. Solder connectors are ok, if you have someone with experience with them.