Someone, perhaps Cook, commented on a thread with a similar question some months ago, noting that there were Confederates living in Queensland after the War.
I don't see that they would have much impact in any primarily White British colony, anymore than other group, unless they went in very large numbers, as they were usually culturally Anglo, so would assimiliate incredibly quickly. Plenty of American traders or adventurers settled in the various colonies with little issue IOTL.
Besides of which, at the time the Confederates would be arriving, the legal framework of their hosts would ensure that they could not implement crazy legislative programmes, assuming they had the power to do so.
However, it would be interesting to see what a large movement to the South African colonies would do. Natal and the Cape would have probably welcomed more Anglo immigrants, assuming there were jobs or opportunity available. A large Confederate Utilander population in the Transvaal would also be an interesting thought, although I would again suspect they would align with the British Utilanders