Jane, congratulations again on your fabulous weight loss!
I hear you on the skin ... I have/had the same problems and yes, it can affect BF readings if the person using the calipers is inexperienced.
In my opinion, the most accurate BF test is the underwater weighing. It's considered the 'gold standard'.
Next are calipers
in the hands of an experienced person, done with a nine-site reading (much more accurate than three or four sites). Someone who's skilled with calipers can usually tell what's fat and what's skin and calipers should be accurate +/- 3%.
I think that BF scales are the most inaccurate way to measure BF. They're all over the place depending on the time of day and your degree of hydration. They're useful for tracking trends over time, however, so long as you use them at the same time of day and under the same conditions.
If you can afford it, what about going for the underwater weighing AND buying a BF scale? That way you could find out your true BF%, compare it to the number on the scale (like 22% underwater = 28% on my scale) and then track the downward trend with the scale, mentally adjusting as you go (does that make sense?)
I've only had my BF done with calipers but there were a few times when I felt embarrassed and self-conscious about the skin. On a nine-site test, you're getting pinched everywhere! It helps if you know the person and feel comfortable with him/her.
I've wondered about something ... excess skin is lean body mass (LBM), because everything that isn't fat in our bodies is LBM (hair, skin, bones, water etc. as well as muscle). So does excess skin skew bioelectric impedance devices downward by making it seem like we have higher LBMs? And thereby give us
lower BF% than we'd have without the excess skin?