If there is enough slack in the current cable to reposition it without splicing, I see no problem with moving it into the wall, in fact, I prefer it that way.
As for the conduit, if the cable insulation is damaged, cracking or otherwise deteriorated, it should be replaced, not hidden in conduit. If it's in good condition now, it should need no additional protection if installed as you've indicated.

Can you clarify a bit?

If you previously had exposed cable coming up through the floor under the sink, it was not to code. It should have come up in the wall to a receptacle where you plug in the disposal, or it should have been in conduit or armored cable if exposed. What was the setup that you are modifying? There is not a problem with relocating a wire as long as it is not installed incorrectly. And the receptacle should be a GFCI.

My house was built in the 70s. The cable for both the dishwasher and disposal come through the wall. Romex, 14/2. No outlet, no box, no GFCI, though the disposal is switched.

"It should have come up in the wall to a receptacle where you plug in the disposal, or it should have been in conduit or armored cable if exposed."

Must be a local alteration.
Cord and plug connection is not required for a GD, nor is armored cable or conduit.