We also tried fixing a handheld Icom IC-A24E Transceiver with VOR capability to the top of the instrument panel, but it gave spurious and unintelligible readings. But I am informed that examiner will also require us to ident the VOR as well, which leads to complications trying to get the audio output through the headsets!
I am confident that with a bit of fiddling you can get this to work well enough to suffice for the few minutes necessary for the flight test. Most transceivers have headset adapters available which may help with this issue. Using a "remote" mount antenna taped to the windshiled (inside) or similar would likely make the VOR signal useable. Perhaps the examiner will let you tune and identify several VORs on the ground to demonstrate that you know how to do this. The bigger question might be whether the examiner is flexible enough to allow some improvisation, given that the likelihood of ever using a VOR (in a VFR helicopter) in this age of the GPS is quite low.
I checked current prices on a handheld transceiver with VOR capability and found a Vertex model for $220 U.S.