The only thing you really have going for you once Nana is gone is your spacing ability (which IC's excel at, because of their awesome WD). Outspace your opponent and strike when you see an opening in their defense.
Your combos are pretty limited solo. Downthrow is usually your best throwing option, as it leads into smash attacks and/or back airs.
When you're alone, take advantage of the fact that you can WD, dashdance, and execute your moves without the need for nana to remain synched. This basically means that you should be able to move faster when you're alone.
WD->Utilt works alright against spacies.
IMO if you really want to see how great a solo IC can be played, watch some Chu Dat.