Having installed a number of mast mount domes I 100% agree with your yard. If you have a conduit, and you actually want the radome wires in it, not slapping the insides of the spar at anchor, then the only way to achieve this is to drop the mast. I have seen yards wrap a halyard internally only to have the owner hoist the sail and rip the dome wire apart. I have seen holes ob-longed and mast tappings destroyed and need to be over drilled due to a boat wake and I have seen crooked dome mounts all from attempting this in a bosuns chair. Also unless the yard specifically and physically KNOWS and remembers exactly what the inside of your spar looks like, where the wires run etc. you run a rather realistic risk of them drilling right thorough your internal conduit and mast wiring, wind, anchor, tri-color etc..
So what happens when they drill the rather large hole, in your rather expensive mast, for the radome wire, and find out they hit the edge of the conduit and can't fit the wire? You now have a useless hole that they will now try to over bore and make a huge mess...
These are all REAL scenarios I have known of or seen happen when an owner tries to take the easier route. Sometimes perceived "easy" is not what it appears.
Can it be done with the spar up? Yes, but it is not a method I would employ.
If you have not dropped it in a while look at it as an opportunity to inspect everything while it is down.
If you had said; "My yard said it is okay to install my dome with the mast up, and it will save me money" I would be hinting at you to find a new yard..