Well, yes, no and sort of... But wee need to examine the three sentences:
Once, when he broke his leg, he made a crutch for himself.
This sentence gives two kinds of information, one temporal, one temporal or causal:
- Time: "Once he made a crutch." Once here means a singular point in time, in this case in the past.
- Cause or time: "when he broke his leg" Depending on how you choose to read the "when" it may also denote a cause, especially if you shift the tense in this subclause to "when he had broken".
Your first variety:
When he broke his leg, he made a crutch for himself.
A simple sequence of events - break leg, make crutch. Not much different from the original, just simpler. The emphasis has shifted slightly to the cause.
Your second variety:
Once he broke his leg, he made a crutch for himself.
Now here something nasty happens. Written like this, the once shifts his meaning to "as soon as". This sounds as if the person in the sentence had made some effort to break the leg (possibly on purpose) and once he managed to do so, he made the crutch.
If you re-write your second example, it doesn't help either:
Once he broke his leg. He made a crutch for himself.
Once gets his original meaning of "at some point in time" back, but the two sentences loose their logic connection, so no alternative either.
Stick with the original or your first variety, ditch the second.