Our 1934 Minnesota home has older wiring. I want to replace the old sconces next to the fireplace with new sconces.

The house wiring at the fixture is cloth covered, with a hot and a neutral (no ground). The old sconce wires (hot and neutral) are tied to the house wiring with a thick covering of tape, and perhaps some kind of coating. I've read this was
Not uncommon back in the 30's.

The new sconces have a black, white, and ground wire. The new bracket that screws to the fixture box in the wall has
A ground screw.

Can I cut the existing sconce wires (hot and neutral) and tie the new sconce wires to them with wire nuts? This would
Mean not disturbing the heavily taped and coated original connection.

Or, do I need to go directly from the new sconce wires to the house wiring (hot and neutral)? My concern there is the brittle nature of the cloth-covered house wiring at these fixtures.

Thanks for your help!

No, you should remove all old wire from the old sconce and wire nut your new black and white to the old hot and neutral from the wall. You have no ground so remove the green wire completely or wire nut the end so it will never short