Is there a safe way of running a fixed wheel without using a lockring?
Yes, with separate brakes on each wheel.
If you have to ask that question you shouldn't try it!
(if you were experienced enough to do it you wouldn't be asking the question)
Because you don't have a lockring thread on the hub? If you ride carefully then using a BB lockring with plenty loctite is OK. Not ideal, but not immediate death either.
Just don't skid.
And don't install brakeless.
@jdp started
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Is there a safe way of running a fixed wheel without using a lockring?