I haven't played WOFF in some time, I lack a good computer and need to invest in a flight stick and equipment, but I was curious about this for some time. When doing a flight where you are the only person flying, does the "No Witnesses" consider that? Or is that option good for those scenarios? My current version is PE.

It's tricker by definition but you can put other great details in to narrow down the location, what happened, description of the aircraft etc (been covered many times here).

In all the yrs I've flown this sim, I have indeed had only ONE victory claim go through without a witness. So it is possible.
If your alone then its up to you to continue or not. The "Claim" can still be put in, as in RL back then, and it looks good on your logbook, having all those claims.
Even Bruno Stachel was told to except the fact that another Tommy was shot down for the Kaiser, but thats it, no claim

Really could do with other means of verifying claims like balloon observer or infantry\arty unit etc.

I find it helps a lot if you staple a $20 to your claim report...

I have shot down a plane that crashed right on top of allied sector HQ, after my flight started going home,
I put in loads of detail about my victim, even wot he had for breakfast coz his #%&*$# was coming back face as I chased him down.
But apparently nobody at HQ noticed an Albatross crashing on there heads.
Vino must have been flowing that day..

This may help get claims approved. Quick claim report/description creator

I am sure Rick_Rawlings is right