We understand this image was taken in late January 1959 during Bill Shatner's stint on Broadway with the production of The World of Suzie Wong. That makes it the most recent toup-less picture we have found thus far. On-screen, he was already wearing a toupee at this point.
Notice how Bill Shatner's real hairline is rounder than the more pointy look that the lace created (this observation was recently made by these folks). That wouldn't last long as he soon started to recede at the front too. If you look closely at the top of the head, it appears that the hair is very short (unable to grow longer), fluffy and thin. The top of the crown (which we can't see) is likely displaying some very noticable signs of baldness.
Above pictures - Studio One: "No Deadly Medicine" (late 1957)