I've got a few lenses with none standard f number sequences on them. They are mostly large format things...
Years ago some manufactures used really wierd methods of denoting the aperture and you get sometimes numbers that make no obvious sense, so you need to consult the sort of table someone has already published, but the traditional f-number sequenced but based on a different starting aperture is no big problem.
I think the traditional sequence (f2.8, f4, f5.6, f8, f11, f16, f22, f32, f45) was only accepted as a standard in 1949? Prior to that the 'continental scale' was also popular (f2.2, f3.3, f4.5, f6.3, f9, f12.5, f18, f25, f36, f50). It seems to tie up better with some traditional lens designs, actually. F4.5 and F6.3 being common maximum apertures for many pre-war lenses. The numbers are still 1 stop apart, they will still represent a doubling or halving of the exposure as you go up or down the sequence, just the same.
If you use the sunny 16 rule you are guestimating anyway. All lenses transmit different ammounts of light depending on how many glass/air surfaces there are and whether and what type of coating. A modern coated triplet will be much faster than a pre-war uncoated 6 element lens (that was the reasoning behind T-stops, wasn't it? But they never caught on...) Additionally, film speed varies with development techniques and old shutters are rarely accurate...
I usually use FP4+ which is rated at EI 125, but few of my shutters do 1/125 sec, so I round to 1/100 when using the sunny 16.
So, it is all guestimation.
Why not just use the sunny 18 rule? If you pictures seem a bit under exposed, half the film speed next time? Or call it the sunny 12.5 rule?
If you want to be accurate with your exposures and meter carefully, you need to do an exposure test anyway to find a film speed. Once you have a speed for a given aperture, regardless of what the number is, just walk up and down the sequence in stops...