Making small changes to the text printed by Print Draft is easy … but only if you or someone you know speaks regular expression talk. This does not affect the text of the project itself, just what gets printed.
Add the following line to PrintDraftChanges.txt in the project directory (create it, if it does not exist)
"\\v \S+\s*" > ""
This says “Look for a \v, a space, one or more things that are NOT spaces(the verse number including ranges and verse segments), zero or more spaces. Every time you find this, replace it with an empty string (effectively deleting it).”