You can't have copper exposed to rocket core temps - it won't give off fumes as such, but will soften and melt; any joints inside the core would be destroyed at much lower temperatures. If the copper is carrying water, the water would flash to steam and explode with any hiccup in flow rate.
I would not just run water to the exterior wall, I would run it to all the places in the house that want warmth, with radiators at appropriate places. Or is it just one big room you want to heat? Running piping in the floor will give gentle radiative warmth, as long as your building construction is compatible.
Air ducting sufficient to heat your house will be pretty bulky, and insulating the stretch between shed and house would make it even bulkier, and may be considered by an overzealous inspector as connecting shed to house and knocking you out of compliance. After all, if a lot of air can move into the house, so can flames (the fact that you can't get flames into the duct if it is properly built is irrelevant.)