Frank Krygowski writes:

It sounds like you're describing some sort of a slot
to allow for wheel alignment. If pulling a wrench
handle moves the attachment point, perhaps you're
applying force parallel to the slot? If so, can you
apply the wrench with the handle parallel to the
slot, and apply force to the handle perpendicular to
the slot? Assuming the width of the slot is close to
the axle thickness, things shouldn't move much in
that direction.

Interesting. So if the handle is put X-ways before the
pull, and then moved into Y-ways, that should minimize
movement along the slot...

Alternately, there are wrenches with T handles, that
allow you to apply pure torque with no sideways
force. Perhaps you can use such a wrench, if
there's room.

Interesting (again). Yes, I have those, but only with
hex keys, not sockets. But perhaps I can assemble one
with bits now that I think about it...

About the nut: It sounds like you're talking about
a serrated face nut:
https://en.wikipedia.org/wiki/Serrated_face_nut
Assuming the metal it clamps against is soft enough
to take a slight impression, this should resist
loosening better than a plain nut plus flat washer.

OK!

But generally, I much prefer other nut locking methods
- say a nut with a nylon insert
https://en.wikipedia.org/wiki/Nyloc_nut

Yes, I have several buckets of those but they are
harder to put in. Also, some people say they can't be
operated several times without loosing their property.
Maybe it is just slander... With them, I take it you
don't need a flat washer?

or (my favorite) an anaerobic thread lock compound.

OK, never heard of

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