Have you seen this tutorial: Replacing the default character with a custom character
if you look at the 2015 method, it shows you how to do it through script. You will also have to make sure that you set the NetworkOwnership to the player by typing in this code after you have changed your characters model.
for _, d in pairs(CustomModel:GetDescendants()) do -- "CustomModel" is where you define your custom model
if d:IsA("BasePart") then
d:SetNetworkOwner(player)
end
end