Whenever I've introduced a new puppy to a home where there is an older dog, I've let the older dog 'find' the new puppy.
EG. placed puppy (usually a little bewildered) in the garden, gone into the house and then let the other dog into the garden. It has always worked. The older dog investigates then comes back to you as if to say "look at what I've found" - almost always in a tail waggy pleased with themselves way.
It can be a good idea to get a new toy for the older dog and act out the puppy 'giving' this to the older dog as well, sort of showing respect.
I would not worry too much about the older one being snappy. In my experience, dogs always recognise that a puppy is a puppy and as such needs to be tolerated and occasionally put in their place if they get bitey etc.
Good luck, I'm sure it will work out