Hi Fiona
This subject has come up pretty often on this forum too
Neutering generally does cause the coat to get thicker & woollier & the changes are more noticeable on those Cockers with thick coats to begin with,which would include most solid blacks. However even with particolours you can see the difference post neutering, though it can take quite a few months for the changes to occur. Most neutered Cockers have to be clipped because it's no longer possible (or fair on the dog) to continue with handstripping. However, there is clipping & there is clipping - as I've said before, some groomers make a horrendous job of clipping Cockers (the shorn lamb look) & others do a decent job, presenting a nice tidy Cocker that still looks like a Cocker.
I think in the post you referred to on the other board, both Cockers had been neutered but only one looked terrible - possibly the other one had a much finer coat to begin with & also goes to a better groomer than the other one
The decision of whether to spay or not to spay is entirely up to you, but coat changes and/or weight gain can be side effects which you have to take into account when making your decision.
As to whether you can now handstrip your girl after clipping her, it will depend on how thick her coat is really. I have stripped out dogs that have formerly been clipped but it's much, much harder with solid blacks & will take lots of time & patience - so not impossible, but may be difficult!
Jane