For furnace ventilation, although it was usual to locate the furnace at the bottom of the upcast shaft, there were instances of a furnace at shaft top being used, with a short stack (circa 30 feet) to ensure draught. Not as efficient as a furnace at shaft bottom but it clearly worked.
But a furnace or powered ventialtion can be dispensed with if only a low volume of air requires to be exchanged and if you have patience. Around 1930 a cousin sank a shaft 100 feet and, as anticipated, broke into old coal workings. He tested the air by lowering a candle in a bucket down the shaft and, as expected, it was extinguished (old shallow workings rarely have methane, only excess Co2 and/or O2 deficiency). He lowered a pipe (6 or 8 inch diameter) down the shaft and let it project around ten feet above shaft collar. In a week or so, the difference in atmospheric pressure plus the wind cleared the old workings. He then applied to the mineral owner for permission to work the coal but was refused. Such a non-furnace, non-powered ventilation technique might possibly have application in the present case?
Have very great caution - there are inumerable instances of well sinkers, miners, and mine explorers descending into O2 deficient or other poor atmospheres and being unable to ladder or prussick out and dying as a result - and not infrequently rescuers going the same way.