[Sharparam]

I thought this would be a lot simpler to implement, but then I was reminded about cross-realm and all the issues that brings. I wrote something up that might work:

-- Add SHARPARAM_GROUP_WHISPER to SavedVariables to persist the settings
SHARPARAM_GROUP_WHISPER = SHARPARAM_GROUP_WHISPER or {}
 
local opt = SHARPARAM_GROUP_WHISPER
 
opt.enabled = true
op*****ssage = op*****ssage or "Welcome to the group!"
 
local members = {}
 
local PARTY_UNITS = {
    "party1",
    "party2",
    "party3",
    "party4",
    "party5"
}
 
-- Helper function to get a list of group members
local function getGroupMembers()
    local result = {}
    if IsInRaid() then
        for i = 1, GetNumGroupMembers() do
            local name = GetRaidRosterInfo(i)
            if not name:match("%w+-%w+") then
                -- Try to get realm from UnitName func
                local _, realm = UnitName(name)
                -- Fall back to using player realm
                if not realm then realm = GetRealmName() end
                name = ("%s-%s"):format(name, realm)
            end
            result[#result + 1] = name
        end
    else
        for _, unit in pairs(PARTY_UNITS) do
            local name, realm = UnitName(unit)
            if not realm then realm = GetRealmName() end
            result[#result + 1] = ("%s-%s"):format(name, realm)
        end
    end
    return result
end
 
-- Loop through members and message anyone new to the group
local function updateMembers()
    if not opt.enabled or not IsInGroup() or not UnitIsGroupLeader("player") then
        wipe(members)
        return
    end
   
    for _, v in pairs(getGroupMembers()) do
        -- New member? Great! Let's message them
        if not members[name] then
            sendMessage(name)
            -- Add them to list so they don't get messaged again
            members[name] = true
        end
    end
end
 
-- Gets the full player name string (name-realm) of the current player
local function getFullPlayerName()
    local name, realm = UnitName("player")
    if not realm then realm = GetRealmName() end
    return ("%s-%s"):format(name, realm)
end
 
local function sendMessage(name, realm) -- realm param currently unused
    realm = realm or GetRealmName()
    if not name:match("%w+-%w+") then
        name = ("%s-%s"):format(name:match("%w+"), realm)
    end
    if name == getFullPlayerName() then return end
    SendChatMessage(op*****ssage, "WHISPER", nil, name)
end
 
local frame = CreateFrame("Frame")
 
frame:SetScript("OnEvent", function(self, event, ...)
    updateMembers()
end)
 
frame:RegisterEvent("GROUP_JOINED")
frame:RegisterEvent("GROUP_ROSTER_UPDATE")
frame:RegisterEvent("INSTANCE_GROUP_SIZE_CHANGED")
frame:RegisterEvent("PARTY_MEMBERS_CHANGED")
frame:RegisterEvent("RAID_ROSTER_UPDATE")
 
SLASH_SHARPARAMGROUPWHISPER1 = "/sharpgw"
 
SlashCmdList["SHARPARAMGROUPWHISPER"] = function(e, msg)
    local cmd, arg = msg:match("(%w)%w*(.*)")
    if cmd == "t" then -- toggle
        opt.enabled = not opt.enabled
        print("Group whisper is now " .. (opt.enabled and "enabled" or "disabled"))
    elseif cmd == "m" then -- set message
        -- dirty workaround to skip the first space
        op*****ssage = arg:gsub("^ ", "")
        print("Update group whisper message!")
    end
end

PLEASE NOTE: I am not sure if this code will work with player names using unicode characters.