WhelanL, IMHO, why go to a 35 Whelan, then shoot light for caliber, old school, cup and core bullets?
The 35 Whelan was developed to shoot heavy 250 grain to 300 grain bullets of that type. Sadly, those weights are difficult to find.
The Barne's 225 tsx, are about the heaviest that are readily available, but Speer and Hornady still make 250 grain projectiles.
I used to use Western Cartridge Company 300 grain bullets and Speer 275 grain bullets in my last 35 Whelan, built on a Remington 700. When I could no longer get them, I sold the rifle.
If you want to use those light bullets on game animals, they might be OK for some of the "cull hunts" you do, but don't load them to the nuts. As you rightfully deduced, they are explosive when pushed fast and were intended for cartridge cases with less powder capacity, such as the 35 Rem and 358 Winchester.
I personally think they're to frangible for the 358Win in strong rifles with fast loads.
"Most" 35 Rem rifles are chambered in weaker lever actions or semi autos, so pressures/velocities were kept low.
If you load to those velocities and take your shots within those limitations on Deer size game they should be just fine out to 200 yds.