The concept of regional style is a much discussed an often misunderstood one. I think in the case of Martin Hayes, you see a player who has taken all his influences and developed them into a personal style. Many of these influences will be the ones he took in when he was (very) young. These will be his local players although perhaps not all of them, and players he encountered through other connections, Tommy Potts for example.
There are a number of fiddleplayers in the mix, that 'lonesome touch' thing is clear in the playing of particularly Martin Rochford, Paddy Canny and is most likely tied to earlier players like Pat Canny (the father) and the man who in turn taught him, Pat MacNamara who traveled the area teaching the fiddle a few generations ago. Other fiddleplayers in the area had some of that touch as well, Martin Woods for one. Those slides may well have been developed on from the ones Vincent Griffin uses in his playing. And there's ofcourse the father, P Joe but I have heard Hayes talk about Junior Crehan, Bobby Casey and the West Clare players as well.
Flute wise he cites Joe Bane as an influence, although perhaps more through his attitudes to music than actual style. It may be worth looking up some of the duets that were recorded of Bane with Bill Malley. Concertinaplayer John Naughton was also in the picture, certainly like he last two as a provider of local repertoire. But I wouldn't underestimate the impact of the musicians who came through the Tulla band over the years either, Hayes started playing with the band at an early age. I have also heard him talk about how the battering some of the West Clare dancers influenced his thinking about the rhythms of the music.
But again, they're all influences that have contributed elements that he combined into his own style of playing. They're all bits you take over time and adapt into your own thinking and playing. And perhaps a regional style is not more than those bits you carry on from local players, things that linger in a place.
It may be worth exploring the styles of some Clare players on the Clare library website:
Clare library : live recordings