"help with drafting" is correct and usable in written English.
For example, "My colleague offered to help with drafting the proposal for our presentation."
Dukureh will return to the Gambia on Tuesday to thank Jammeh for the ban and to help with drafting the legislation that will enforce it.
MM: Study concept, design and coordination, collection and interpretation of data, help with drafting the manuscript, critical revision of the manuscript.
We can provide advice on gaining access to restricted use data and help with drafting agreements for using it.
He supposedly picked the uniforms (though we might assume his wife, Gaynor, had a significant input), he sorted out the hotel accommodation (though we might assume a European Tour lackey or six had a significant input) and he delivered a speech at the opening ceremony (though I'm guessing he might have had some help with drafting it).
VLC: analysis of the histological data help with drafting of the manuscript.
MMM: analysis of the molecular biology data and help with drafting of the manuscript.
