On a giant 50 mile high volcano, created and sustained by magic, there is extreme weather. Storms, high winds, snow, everything you'd find at the flanks of exceedingly high mountain. Explorers have started to push up the flanks, trying to push the bounds of how high they can go. Like all alpine explorers they are acutely aware of the weather and it's ability to impede their progress.
These explorers have :
No breathing equipment in the form of space suits or supplemental oxygen
Standard alpine equipment for the 1940's
Standard issue human bodies that are well adapted to life at extreme altitudes
The volcano itself is no steeper than 10° and usually around 5°. Climbing it is more akin to a shallow hill rather than what people usually think of mountain climbing.
My suspicion is that a human climber could get high enough on the sides of this volcano that the line between (barely) breathable atmosphere and hypoxia is the difference between a high pressure front and a low pressure front.
At what altitude on this volcano would a low pressure front, in and of itself, be lethal?
Although Mount Everest at around 8000m has been climbed without supplementary O2, the very low O2 partial pressure at the summit means that it is at the limit of man's tolerance, and even day-by-day variations in barometric pressure apparently affect maximal O2 uptake.https://www.ncbi.nlm.nih.gov/pubmed/6863078
So at 8000m you are already in the zone where variations in barometric pressure can affect you. Anything that can affect maximal O2 uptake under such extreme conditions could easily be fatal.
It is hard to be precise because it depends on so many other factors such as how fit someone is, their genetics, the temperature, the wind speed, the latitude of the mountain and their level of exertion, but even allowing for the fact that your mountain is a gentle climb, by 8000m you would be in the death zone for sure and slight changes in pressure would be significant.
There are no high and low pressure fronts, there are high and low pressure areas. The pressure disturbances associated with fronts aren't strong enough for a real effect, you want to look at strong pressure gradients between high and low pressure areas.
At a height of 7 to 8km you are close to the jetstream level meaning your explorers could be exposed to hurricane-force winds, like on Mount Everest. And jetstream-force winds don't just appear around low pressure systems, they can be found in a much wider area. This map shows low pressure at the surface and associated jetstream at 250hPa pressure which is around a height of 10km.
Back to pressure gradients:
Usually pressure in the upper atmosphere is written as the geopotential height of an imaginary plane of constant air pressure, and it is expressed in geopotential dekameters. Like this a pressure gradient can be related to a change of height. If you had a strong low pressure system going "over" your mountain you can have pressure gradients that correspond to a height difference of 500m over the course of 24 hours. That's a very rough estimate though.
You have other problems
A low pressure system can't go "over" your mountain, your mountain is such a major obstacle that it will strongly modify all atmospheric events, I don't really know how a low pressure system would behave if it met with your mountain, my guess is that it would be lead around the mountain by the associated jetstream that would also blow around the mountain then, so that its low-pressure core wouldn't hit the mountain at all. You main problem then will again be the wind. And with the Hurricane-force wind there also comes extreme wind-chill.
Mount Everest was first climbed in the 50s, so if your explorers have 40s equipment it will be hard. Also Mount Everest is surrounded by other mountains that provide additional protection, your volcano is a singular peak, air can flow freely around its flanks. Unless there isn't a stable wind direction so that they can climb in the lee region of the mountain they would have deal with those winds. And passing low pressure systems would mean changes in wind direction and increasing wind speeds.
Even while the pressure gradients are comparable to significant height changes they don't matter much because the associated winds would be the much bigger problem.
If you get pressure gradients, you get winds. If you put your mountain into a calm zone you don't get dangerous winds but also no significant pressure gradients.
Anything above 8000 meters is called 'the Death Zone'. People can be there, but only for short periods. Altitude sickness is worst when you sleep - if you go to fall asleep that high, you'll probably die.
Mt. Everest can be climbed without supplemental oxygen, but climbers sleep at a lower altitude (starting from around 7500, ascending to the top and then quickly descending back to at least 7500, probably lower).
Your mountain isn't technical nor particularly hard to climb. On a good day, an explorer might start from 7500 meters, push to 10km or so, then go back down - possibly way down, lowering the risk.