My initial thoughts based on vague recollections areas follows.
Hopefully someone that has done this more recently can check my work, but I'm pretty sure this is right
You'll need to re-write the bios chip on the cart to accomplish this - there are lots of different bioses to choose from here
https://www.arcade-projects.com/threads/cps-iii-bios-and-cd-releases.36/ Which one for your use case?
Because you have an original cart you are going to want one with the CUSTOM SH2 - this was a custom chip for Capcom that they put into these carts. If you had a repro you would want the "standard SH2" but you don't so you won't.
Because you don't want to read the CD drive you are going to want the NO_CD version
Because you don't want to select the region on every power on you are going to want the superBIOS
Because you don't have Ultrasims you could use either the ultraBIOS or the superBIOS
So putting all that together I believe you will be wanting
NOCD USA SuperBIOS for Custom
which you can download here
http://www.mediafire.com/file/x0qul3rlzfje8bn/SuperBIOS_NOCD+AsiaNOCD_Custom&Standard_.7z/file
Then you will need to physically remove your existing BIOS chip by desoldering it off the board inside the cart,
write this file to the chip
SuperBIOS_for_custom_SH2_USA_NOCD.u2 (or obtain a new bios chip that someone has already programer with this file)
Solder the new/updated chip back onto the board
Done!