Yes, I am talking about the same source. The Robert who married Mary Egerton is the later one (son of James II) Walter Harris was talking about the sons of Sir James I when he says only 1 son had male issue. (That son obviously being Sir James II; inferring that if Robert born 1602, was a son of Sir James I, he had no male Ware descendants.)
If, by discrepancy, you refer to there being no son Robert attributed to Sir James I on Wikitree, this may be because there is insufficient evidence. As I mentioned, his possible son Robert only appears in Burke’s with a caveat attached. It may be that this is the only source for a Robert, and there are other sources that argue against there having been a Robert. You may want to contact the profile managers to see if they have more info.)
Alternatively, if you are talking about there being no son Robert attached to Sir James II’s profile, he is mentioned in the biography, & I would imagine no one’s got round to adding him yet.
I had a look at the Wilder Book (the link below is a later edition, published under a different title), I can’t see any citations for the Ware genealogy. The book also says Sir James I only had 2 sons & 1 daughter, which clearly isn’t true. Peter Ware (also mentioned in the book) seems to have now been attached to an altogether different family, so what is left that seems creditable? (It’s claims about the Wilder origins are iffy too unfortunately.) https://archive.org/details/wildersomeconnec00wild/page/16
The trouble with these genealogy books is that usually the later generations have been sourced and can be corroborated & that lulls readers into a false sense of security about the earlier generations, which, more often than not, are junk. (The internet has added to the problem - much of this junk is then put into trees and copied multiple times. So we have what looks like an independent corroboration of ‘facts’ from multiple people, when actually it’s still the same one piece of junk in repetition. A loop tape of junk. Even junk that was discredited many years ago still finds its way into trees today, as the next generation ‘discovers’ the old (discredited) book on the internet.)
What I am trying to say is, don’t send yourself on a wild goose chase on the basis of an unsourced book. Life is too short.
Do you know if any descendants of Robert or Peter have joined the Ware DNA project on Familytreedna.com? Maybe their Ydna has already been compared?