You can often remove the NDS cones and pull the axle out of the DS side.

My guess is your axle has a grease seal on the right cone. Was there a grease seal attached to the left cone?

You could probably pound the cone out of the grease seal, but you won't have very good access to anything.

Assuming this is a modern splined freewheel, it is time to break down and buy the tool, or find someone to borrow one from.

For freewheels, you only need the tool to remove the freewheel, and can put it back on without the tool, so you could do a quick run to a bike shop or bike co-op.