The Straight Razor Place Yahoo Group and Wet Shavers on MSN Groups are generally considered the oldest wetshaving forums. Both predate The Straight Razor Place and Shave My Face forums. That is assuming you consider MSN Groups and Yahoo Groups to be forums. I do, as they had the same general layout. Charles Roberts, a barber in Austin, Texas who created "Method Shaving" apparently had a short-lived MSN shaving group even before Wet Shavers (ref.
Sharpologist). I never saw any other mention of this group, and do not know what it was called.
Suffice it to say that the Internet aspect of the current wetshaving culture had its roots sometime in the mid to late 1990s. That was also the time frame in which home Internet access became widespread. "The Straight Razor Place Yahoo group and Charles Roberts' MSN group in the late 1990s" is likely as good as an answer as you will get.
BTW - The Straight Razor Place forum - the real Straight Razor Place forum at the original URL - is now back online.