If you want to create a serene and tranquil sense of occasion you may want to do without a ceremonial procession entirely.
If so, you can have the coffin brought to the venue before anyone arrives, or bring it yourself.
As people arrive they can simply come in and sit down and be contemplative. The right music will add to the mood. The ceremony can begin when everyone is ready.
This sort of atmosphere may be particularly appropriate in the case of someone who led a simple life and died at a great age.