しのぐ itself means 'overcome', 'overtake', 'stand for it till the end' or something such. Without the context, I can't be sure what it really means, but here is two interpretation. 1. Unless we put through the song.... (if another sentence follows, probably this is it.) 2. We have to put through the song. (if the sentence ends itself, probably this is it.) I wrote PUT, but please modify the verb to fit the context like 'sing through' or 'dance through'.

Hopefully, someone will see your answer. By the way, Javanese is spoken in Indonesia - it's not Japanese. :)