[Jim McDougall]

Guys, all excellent interpretations and suggestions, and I hope I may add mine after going through "Catalog of European Court and Hunting Swords" (Bashford Dean, 1928).

With the artistic range of these kinds of pretty exclusive sword hilts, it would be pretty much impossible to find an exact match to this one. The double headed eagle in the motif is tempting yet misleading. If we attempt to place it specifically in accord with the known heraldic arms of Russia, and Austria as noted, as it is not exact in its form with exceptions in its elements it is speculative only.

The features in the motif are very unique, and unlike most themes on other European court and dress swords. In the reference (Dean, pl.XXXIX,#50) there is a N.European (German) example which has similar baroque styling in the shell guard rather than the standard bilobate type, has a 'boat shell' like form which seems rather unusual in these hilts.
This one dates c. 1780.

In another example (Dean, pl.LIII, #70) there is a French example again elaborate baroque styling and the pas'd'ane is more 'squared' with similar type ribbing in these structural elements. This example from c. 1770 has associations with diplomatic circumstances and a secretary of state of Russia.
The period of this example in those may extend into early 19th c.

I would suggest that this example might fall into this type of category and these influences may have been added into the design. Possibly the deviation in the eagle might be simply artistic license? The royal connections in most of these countries and diplomatic channels seem to be a good explanation for hybridization and influenced styling. In any case. likely third quarter 18th c.
Possibly heraldic sources might offer more specific look at this unusual eagle design.
Oddly, there does appear to be use of the 'Byzantine' double head eagle in Masonic regalia, so this might be a variation of those.
Usually there is one sword held horizontally.

The hexagonal blade seems unusual as well, and it seems the 'concavities' feature with these ellipses in linear grouping is something I have seen on some European blades but in a floral type configuration.