You probably have a 110bcd crankset. So, 34T, or maybe 33T is the smallest you can go. For smaller chainrings, you'd probably have to change cranksets to a triple.
Here are the Tiagra specs.
RD-4700-GS
They should support a 34T rear cassette. Also 39T to 41T total chain wrap.
(50-34) + (34-11) = 16+23 = 39T. and it should be supported by your derailleur. Anyway, you're close enough that it is worth trying out..