Either you whistle before you pull the trigger or you have one mighty slow 22-250.
Whistling to get my prey’s attention is a trick my Dad taught me, hunting Cottontails.
Get the shot framed, animal in the sights, whistle gently (and low pitched - a high pitch may make them run). It doesn’t have to be loud, in fact it’s better if it’s at the level of a loud whisper. That way, it sounds more distant.
The animal will typically think “What was that? And where did it come from?”
Then, a moment later the lights are out - fast, painless, clean. Best part - Zero wasted meat.
I like the 22-250 for Whitetail Deer. It’s not a good long-range weapon (IHMO, your opinion may vary) - but it was the rifle that was available from a kindly neighbor. But, it’s been years since I’ve hunted. Right now, if I were to get back into hunting, I think I’d go for something a wee bit bigger.