I have a fairly old house (100 years this year) and there's no hot water in the upstairs bathroom sink. It comes out at a very light trickle. I'm pretty sure the rusty clog is just inside the wall or under the floor.

My question is, can I just cap off the hot water line and install an instant hot water dispenser? I figure if the cold water flow is sufficient it couldn't hurt to split it in half and use it as a hot water source.

I don't want to replace the pipes because, to me, it's easier to run an electrical line then to crack open a plaster wall.

Notes:
The cold water line is fine. Plenty of pressure/flow.

I know its in the wall and not on the sink side. I cleaned the faucet and replaced the supply line and shutoff valve. The old ones were clogged with rust.

The shower in the bathroom is OK. OK enough to have a fairly hot shower in the winter.