If file size is an issue, a gedcom file is about the same size as a PAF data file. An advantage of a gedcom file is that it can be read by all genealogy database software.
To create a gedcom file in PAF: Click File menu > Export, then select All or Partial. (If you select Partial you will need to select what family lines and what data you want to send.) Click Export > select a location (I suggest the Desktop) and input a file name for saving the gedcom file. (Be certain to REMOVE the * from the file name or the process will fail.) Click Export and wait while PAF counts the records being exported. When the process is finished click OK (or Done). You will now have a brand-new gedcom file saved in the location you chose with the name you chose.
You can now attach it to an email message or put it in your Public folder in Dropbox.