Based on what I know from BrdU / CldU/ IdU staining experiments, you should see SOME signals (corresponding to the fastest forks) even when incubating as short as 10 minutes, and probably 5.

But this poses two problems : (1) the error that you make when measuring fork velocity increases for shorter incubation times, and (2) because of the resolution of DNA combing (~2kb), some signals will be difficult to discriminate from background.

Of course both concerns depend on the fork velocity in your cell type.

we are using it only for replication fork and origin studies. I think that the bottle neck in this procedure  is to obtain long and intact dna molecules.

No. although getting higher density of molecules ease teh analysis.