For sensitive information, you could send an electronic copy via a shareable link in a cloud drive service (Google Drive, Box, etc.) and then restrict the link to the recruiter's email or make it a temporary link.
Alternatively, you could use the following code in Adobe Acrobat to make a resume PDF expire at a certain time (credit at the bottom):
// Set the date you would like it to EXPIRE ON.
var d1 = util.scand("mm/dd/yy", "7/1/04");
// Let the script do the work...
var expire_on_X_days_left = 0;
var d2 = new Date();
var diff = (d2.valueOf() - d1.valueOf()) / 1000;
var daysleft = ((diff / 60) / 60) / 24;
if( daysleft > expire_on_X_days_left || daysleft == expire_on_X_days_left )
// Comment this line if you would like it to NOT MAKE A BEEP!
// Uncomment this if you would like a message to be displayed.
// app.alert("This document cannot be viewed anymore.");