I don'the think there is an automated way to do that in Timeslips.

Also, why would you need them to go to you first,  if you are just going to then forward them?

Just print the drafts to a PDF, save the resulting file,  and attach it to your email to the lawyers for their review.

Another option , if the lawyers are all part of the network, is  to save the pdfs to a folder  on the server where they can read them directly.