No, you can't combine the two circuits because of NEC 300.3(B). (funny I was just answering another question about that one). It says all related wires must be together in the same cable. But also, they must be in the same circuit.
That bare "ground" from the wall
Now, if the ground wire from the wall is bare, it's probably illegal. When grounding came in in the 1960s, they did a bargain with appliance makers to continue allowing 3-prong H-H-Neutral connections, but with a big asterisk, and the asterisk was to start using 3-wire+ground cable as soon as stocks of the old cables ran out. So at least someone could convert to a safer 4-prong connection later. The legal cable types were:
- SE service entrance cable (in small sizes) -- two hots and a bare neutral in a mesh around the hots. This is made for the service entrance or lateral from the utility, which supplies 2 hots and a bare neutral. If this is the type of cable you have, then it's legal to wire N+G to the bare mesh Neutral... but only because you are grandfathered.
- /3 no-ground cable -- insulated white neutral. Deprecated because /3 has ground now.
- /3 w/ground cable, when stock ran out of the above cables. The ground went unused.
- NEVER legal: /2 w/ground cable misusing ground as neutral. Ground can't be re-tasked to be neutral.
Some electricians felt the other cables going out of stock was their "license" to use /2 w/ground. Wrong.
However... /2 w/ground actually is fine for a 240V-only range.
So if your cable is /2 w/ground, then something goes in the trash, either the cable or the neutral-hungry oven/range. Either replace the cable with /3 or get a range that is 240V-only.
If your cable type is SE (meshed neutral), then you have an option... but not quite as good. You can carefully insulate neutral, and then retrofit ground by running a #10 ground wire from that location to anywhere else that has a #10 or larger ground wire going back to that same panel. The list of possible appliances are water heater, dryer (if it's not in the same pickle), air conditioner, any non-flexible metal conduit, or the bare mesh copper "Grounding Electrode System" carrying ground out to the water pipe or ground rods. You need a split-bolt to tap the GES, you must not cut it.
Another very, very wackadoodle option, if you have the oven's schematics, is to re-wire the oven so the 120V loads on the oven are completely separated from the 240V power going to the oven heating elements. This may be quite easy if it has a big 2-pole contactor to control oven power. Now you can have two line cords - a NEMA 5-15 common recep with H-N-G that runs everything but the heating element -- that can go onto any 120V circuit including kitchen recep circuits........ and 2 fat hots and a ground which can go to that /2 cable. This must not have any conductors tied together or in common, except for safety ground.