Yes, the new I797 approval notice along with the old visa stamp is good enough for re-entry at the immigration. I used my previous employer visa along with my transfer approval notice until the old visa expired.
Please check this with your company immigration lawyer, they will also state the same. No need to spend unnecessary money to get it re-stamped, when you already have a valid visa of the same type stamped in your passport.
Technically, you transferred the old visa to your new employer.