If we are restricted to online audio resources provided at somebody else's expense, the options are of course limited. There is in any case, so far as I can tell, no internet 'radio' devoted solely or even largely to traditional unaccompanied singing; the average 'folk' listener seems to find that sort of thing too challenging, so demand is relatively small. 'A capella' is a term more usually applied to other genres, so unhelpful here.

There are however a number of very useful resources provided by well-funded American institutions such as the Library of Congress. All have been listed in past discussions here (some quite frequently, indeed) and range from collections of ethnographic field recordings to archives of printed music. A list of links to many of the major sites, with brief descriptions, can be seen at

http://www.folk-network.com/directory/links/song-collections_web.html

These are recordings of real traditional singers in the main, so sometimes a bit rough and ready. Very useful for somebody looking for less well-known material, though, particularly in an American context. I believe that Mike lives in the USA, so he should find such things as the Max Hunter and John Quincy Wolf collections particularly interesting.