Yes it could. 'When' would also be a valid alternative.
Both 'when' and 'while' can be omitted only if it is clear who or what the modifying phrase refers to.
In your sentence, 'while' or 'when' is omitted since "trying to catch knives" can be attributed to "people in cooking school". However, this relies somewhat on common sense, since syntactically it could be argued that it is the "stuff" that is trying to catch knives.
This answer presents the perils of omitting 'while' where context (or lack thereof) doesn't allow for easy understanding of the meaning.