There was certainly a system of apprenticeship in place in Ancient Egypt, although there doesn't seem to be any evidence to support the idea that people travelled any great distance to train as artisans.
We have good evidence for apprenticeship contracts from the 18th - 20th dynasty Workmen's village at Deir el-Medina. There is a good overview of what we know about that site in Kathlyn M Cooney's excellent paper Apprenticeship and Figured Ostraca from the Ancient Egyptian Village of Deir el-Medina [Willeke, 2013, p145]. The workers of this village were particularly skilled artisans, and children were apprenticed to other families in the village to learn their skills.
In the later periods, we have a pretty good overall understanding of the apprentice system that was in force in ancient Egypt during the Roman period. Once again, children seem to have been apprenticed locally to learn their skills. This does not mean that their training was necessarily carried out locally. Smiths and potters would certainly have been based locally. The same is probably true for boat-builders. However, masons, for example, might travel considerable distances to work on commissions, and their apprentices would accompany them. A good, accessible paper here would be W. L. Westermann's Apprentice Contracts and the Apprentice System in Roman Egypt.
Although not really artisans in the traditional sense, the only "trade" that the ancient Egyptians seem to have travelled any great distance to learn is that of the scribe. There is some good evidence for scribal training being carried out in a town or city that was not the apprentice's home town. Ronald J. Williams' 1972 paper Scribal Training in Ancient Egypt is available to read free online if you'd like more information.
- Wendrich Willeke (ed.): Archaeology and Apprenticeship: Body
Knowledge, Identity, and Communities of Practice, University of
- Westermann, W. L: Apprentice Contracts and the Apprentice System in
Roman Egypt, Classical Philology, Vol. 9, No. 3 (July 1914),
University of Chicago Press, pp. 295-315
- Williams, Ronald J: Scribal Training in Ancient Egypt, Journal
of the American Oriental Society, Vol. 92, No. 2 (April - June,
1972), pp. 214-221