There are three likely Births in Inverness(shire) inclusive of Skye, in the period 1910 to 1915 inclusive, on Scotland's People - which gives direct access to the official Statutory Records of Birth, Marriages and Deaths for Scotland.
To be certain that you are following the correct line, you should try to locate any later records, such as Marriage and Death, probably in the Canadian Archives, if the Prince Edward Island connection proves correct.
The Death record can be particularly useful if similar to Scottish records; and IF the INFORMANT knew your gradfather's particulars accurately.
The more information that you can obtain on his (Canadian) life, the greater the chance of following through accurately in to the Scottish records.
Have you any idea of his age when he migrated; and were there others with hin. If Adult, his Occupation or Trade etc.