Raising greenfees is all fine and well, but to do so only for overseas visitors would IMHO be a big mistake. First, there are the logistics - how to make sure who is overseas and who isn't? Will you do it on nationality or accent? Am I overseas, coming from Germany? Are the Irish? Or is it just Americans, who have to pay more? But what if they live in Scotland? This "finding out what price you have to pay" could become extremely awkward for the staff and make visitors feel less than welcome.
I am talking from experience, because we have a scheme here in Germany, where we are divided into first, second or third class golfers, depending on the club we belong to and the membership dues we pay. And some German clubs charge higher greenfees to second and third class golfers. The result is that many of them won't ever go to play at these clubs. Even if the price difference is just 5 or 10 quid, it makes you feel second tier and unwelcome.
What I would do is not sell greenfees, but memberships. Put the yearly membership price at what you would like the greenfee to be. It might encourage some visitors to stay longer or return later in the year. And THAT would be the boost that the local community needs. All others, who just want to play a once in a lifetime round, at least get a memorable member's badge to display on their bag. Which will lead to their playing partners asking what the hell Askernish is ...
Ulrich