Is there a single-character convention for the weekdays?
Yes, pretty much all dialects of English recognise the initials of the week-days.
Two- and three-letter abbreviations are also common. To use
Su M Tu W Th F Sa to differentiate those days with the same initial, or just
S M Tu W Th F S which does the same but doesn't worry about the weekend days, is rare but not unheard of.
Would M T W T F S S be confusing?
No. Nor would
S M T W T F S. This latter is more common in English-speaking countries as a convention, if there's no need to stick to any of the standards that insist on Monday as the start of the week, and even if there is (that information can be overlaid on the more conventional layout if necessary).
Other permutations would be rarer though,
S S M T W T F would be less easily read and
T F S S M T W had better have a very good reason for being used.
There are places that use
M T W R F S U but this is mostly when a one-character unambiguous letter is needed outside of a context that helps explain it, and to be strongly avoided in any other case.
If you may need to internationalise this UI though, you may find that other languages don't handle such heavy abbreviation as well. I'd at least allow room for Dé hAoine to become hA if other languages may need to be considered.