There are no extant parish records for Portree that would verify a birth around 1800, unfortunately. What is, of course a matter of historical record is that there was mass emigration of MacDonalds from Skye (particularly from Sleat) in the late 18th century as the MacDonald landlords saw their land as more valuable than their tenants and were pretty ruthless at evicting those who offered no economic benefit.
Your family tradition is wholly plausible but I suspect that finding evidence top prove it might be impossible.
Thanks, that matches what I've found. The Portree and Sleat parish records have a limited date range
114. PORTREE
114/1 Births 1800-19, Marriages 1800-19
114/2 Births 1819-54, Marriages 1819-54
115. SLEAT
115/1 Births 1813-19, Marriages 1813-17
115/2 Births 1819-53, Marriages 1820-52
An Archive Assistant at the Skye and Lochalsh Archive Centre confirms that the date ranges for the other parishes are limited as well.
Bracadale (1802-1854); Duirinish (1817-1854); Kilmuir (1823-1854); Snizort (1823-1854) and Strath (1820-1854).