That actually requires tweaking the mod itself in code, a far as I know.
Look for the following code in the GuildRaidSnapShot.lua file in the Addons folder.  It's around line 116:
function GRSS_ChatFrame_OnEvent_Hook(event)
	if event == "CHAT_MSG_WHISPER" then
		if ( GRSS_IsWhisperGRSSWhisper(arg1) ) then
			return
		end
	elseif event == "CHAT_MSG_WHISPER_INFORM" then
		if string.find(arg1,"^"..GRSS_Prefix) then
			return
		end
	end
	GRSS_ChatFrame_OnEvent_Original(event, arg1, name);
end
And change it to this
function GRSS_ChatFrame_OnEvent_Hook(event)
	if event == "CHAT_MSG_WHISPER" then
		if ( GRSS_IsWhisperGRSSWhisper(arg1) ) then
			return
		end
	end
	GRSS_ChatFrame_OnEvent_Original(event, arg1, name);
end
That should allow all outgoing GRSS whispers to display to you as well.