There's no real weather - so no real rain, at least none in the amounts needed to make a river. It's like living in a sealed jar. So there's no naturally occuring rivers. And no underground rivers (supplied by rain etc) to produce naturally occuring springs. I could see an underground open portal to someplace wet producing the environment you're looking for though.
Presumably there's some water flows in Undersigil - maybe a tributary of the Styx that enteres through aportal - but all the water (like all the air, soil, wood, stone, food, beer...) in Sigil is an import, be it so much as a fountian that's a continually open portal to the plane of Water.
I think the only thing really defined for Sigil is the Ditch, at the edge of the hive- and you couldn't swim in that normally, anymore than you could swim in the Ankh River (from Terry Prachett's Diskworld books in the event you haven't read 'em)