I've had two surgeries on my shooting shoulder. So over the past 4-5 years have used most all of the smaller cartridges. Never had any trouble with killing deer. Use a good bullet and stick it in the right spot.

I've used the .223, 22-250, 6mm TCU, 6x47 Rem, 25-45 Sharps, 25-35 Win, 6.5 Grendel, 7mm TCU, 30 Carbine, .327 Federal, 357 Mag, 350 Legend and several others.

Use the recoil calculator. https://shooterscalculator.com/recoil-calculator.php

For me anything under 11 Ft.lbs is comfortable.

The past year I've used a Tikka T3x lite chamber in .277 Wolverine to take several nice bucks. Also used a Henry All-Weather 45 Colt with Barnes 225 XPB.

I've sent my Tikka in to have a new barrel installed, chambered in 300 Ham'r. Time to try something different.