Absolutely Glen, research never stops!!!
The 'spadroon' shown in the top picture I believe is British as the 'cigar band' affectation did not occur elsewhere, as I understand. Interesting image of Pegusus (?) in the guard, and I am wondering if this might have been special order (as I believe these were) possibly to a yeomanry officer? Returning to Masonic, and even perhaps heraldic symbolism, which such unusual image might have associations with, there were instances where the lodge sentinels, the Tiler, actually had swords made for thier duties. Again, the sword could certainly have been worn in regimental duty as well.
The second sabre seems profoundly French, the black ebony fluted vertically is an affectation seen in many French sabres of the turn of the century. Also the blade in cross section with fuller to centre point is the Montmorency cross section I believe, also of this period. Interestly James Wooley of Birmingham often used this style cross section in his blades, so there remains that possibility.
As devils advocate, I have found some information that may subscribe to the aesthetics approach, and I include it here as I think it is important to present all possibilities whether for or against a theory.
In going through many references on smallswords looking for possible examples using this type of motif, it is interesting that the late Mr. A.V.B. Norman, one of the most astute scholars on hilt forms, does not make specific mention of any possible symbolism in these five ball hilts. I looked through both his "Smallswords and Military Swords" (1966) as well as the magnificent "The Rapier and Smallsword 1460-1820" (1980) which revealed no mention than the obvious description using the motif.
It does seem that smallswords of the 18th century, and particularly after the advent of the rococo period, showed an affinity for representation of paste jewellery, indeed many hilts were fashioned by jewellers. The closeness of beads to images of pearls is quite clear, and in certain Eastern swords with bearings enclosed in open channels the beads are often called 'pearls'.
The fascination for the Eastern European hussars and thier sabres was well established and their flamboyant fashion much admired.
One very important and well known regiment was that of Esterhazy's Hussars in mid to latter 18th century. The sabres of officers of this colorful Hungarian regiment (as seen in Wagner "Cut and Thrust Weapons", p.406, pl.36) has a string of beads (pearls) extending the length of the knuckleguard.
Whether this rather ostenascious style extended into the sabres of other officers of the time is unclear, and it hardly seems that this affectation on a single type of sabre used by the limited number of officers might influence an entire sword style. However, it does seem that the motif did appear in a number of places, which may have entered into the design.
Returning to Masonic possibilities, it is the numeric that is key, not the element of motif.
All best regards,
Jim