I need the glass panel on my door replaced..who to call?

It’s a very nice Craftsman-style mahogany door with a rectangular panel of triple-glazed stained glass at the top 1/3 of the door. The glass has smashed into a million bits (tempered glass) and now I need to replace. I can get the new piece of art glass from the manufacturer, but what type of professional do I call to take off the mouldings around the glass and remove and put the new glass in? I really want someone who has respect for the mahogany door and won’t do any harm to the wood surrounding the opening. Unfortunately, the door manufacturer does not have their own people to replace broken glass panels. They also offered no referrals. I called today. They claim it’s easy to do myself, but I’m scared of screwing it up.