What would be the difference between "Celtic" and "Western European" style?
It seems to me, e.g., that GHB, Veuze and Gaita are much closer related to German Schaeferpfeife, Flemish Pipes, french Cornemuse de Centre, Spanish/French Boudega, other non-Celtic Spanish Gaitas, than to Uilleannpipes (let alone SSP, which seem a lot closer to German Huemmelchen than to GHB!). I don't see anything distingiushable "Celtic" about the pipes from Celtic regions - not even the repertoire of music, since esp. in Breton music, it all blends together - in a typical Breton way
However - I'm at the moment thinking into an entirely different direction - I'd be thankfull for Your help, if I made any mistakes there...
While generally it is true, that instruments do change more within time - and less when spread too far too fast - what started me thinking is:
There are bagpipes the US or Australia for almost three centuries now - but nothing like an "American" or "Australian"-type of bagpipe has evolved. Why?
Probably because the people playing it wanted to show their being part of a certain culture (usually Scottish/Celtic).
Now - what if that was just the same in the middleages?
What I mean is this: We know very little about how the bagpipe came to Europe north of the Mediterranian - except for the fact, that they were neither pictured nor mentioned before about 9th/10th century - the time, when contacts between Northern and Mediterranean culture intensified.
The "Western European"-type seems to appear about 11th century - the time, when through the crusades there was more contact to mediterranean area (where single-reeded bagpipes as well as double reeded "Zurna"-type-shawns existed since at least 200 b.c.!) than in all centuries before. I also recall the usual pictures of bagpipes at this time (migh be wrong, feel free to correct me
) being rather in courtly context, unlike 3 or 4 centuries later, when we see them in a rather peasant context.
So - my idea would be: Like Scottish pipes today in the US or Australia, in the Middle-ages, the Western type of bagpipes did not change - not because it was spread so quickly, but mostly, because it was a sign of a certain knightly or courtly, at these times already very international culture.
An indication to that theory would e.g. be the form of the Latvian bagpipes today. While the (rural, ethnic) music-repertoire played on it is quite similar to bagpipes of nations around it (Dudmaisis, Torupill), making construction and fingering of the chanter (almost) identical to these, the outside design is entirely different - it looks exactly like the Western European type of the late middle-ages! Is it a surprise, that the area of nowadays Latvia used to be a stronghold of Western-European knights right until 19th century?
Also, we have a hellenistic figure, dated 2nd century b.C. in a museum in Berlin from Egypt, playing a droneless bagpipe. So, first mentions and iconography come from greek-influenced mediterranean area, centuries b.C. Also, Nero's pipes had been named by Dio Chrysostomos and Martial with Greek names, thus pointing them out as Greek instruments. So, yes, first mentions of bagpipes do come from Europe - but not from Northern or Western Europe, only from the mediterraneans. There is not a single sign of bagpipes anywhere else before a millenium later - when contacts to mediterranean culture intensified! 
