At what frequency?
Insulation thickness and dielectric constant determine impedance of the pair (assuming this is a TLT), which has impact on the matching and balance towards the high frequency cutoff (1/4 wave point) of the transformer/windings.
The dielectric should generally have low tan delta (silicone is probably okay?, PVC is bad, others are generally okay to great), and the wire spacing and k should be selected to give the desired characteristic impedance, give or take a modest margin.
As for its other properties, silicone I suppose doesn't do you any good here. You can't run at high temperature (besides solder melting, resistance rising, and corrosion at temp, the ferrite core has a relatively low Tc being a NiZn material), and its chemical inertness / environmental resistance is hard to harness without potting the whole thing. If you have it on hand---it's fine, you just aren't taking advantage of these properties.
Wire stranding probably makes no difference; it has a small advantage at medium frequencies where the contact resistance between strands is high enough to give a *little* bit of litz effect (generally in the 5-15% range), but I'm guessing from the core, this will be at frequencies where this doesn't matter. Or maybe solid is in fact better, because of the smoother surface (whereas the rough surface of a stranded wire causes current to flow preferentially by the outer peaks, and over a longer distance along the valleys). If nothing else, wind both kinds and measure the insertion loss!
Tim