Can a manager reduce my work hours because there has been (unverified) issues with a coworker?
No. This sounds in violation of section 83(1) of the BC Standards Employment Act and section 2.8 of the BC Occupational Health and Safety Regulation. Your situation altogether reflects the employer's awareness that "a complaint or investigation may be [...] under [the Standards Employment] Act" for the employer's failure to properly address the issues the coworker is causing.
This is another reason why you really should not acquiesce on the requested statement about you being "satisfied" with the manager's resolution. Complying with the manager's request will give her the opportunity to falsely allege that your statement was in reference to her "resolution" or settlement/agreement as to a reduction of your work hours and that you belatedly "changed" your mind.
Can she offer the ultimatum "work with him or have your hours reduced"?
She can make a proposal of that sort. However, positing it as ultimatum contravenes the statutes I mentioned in the other answer insofar as the employer knowingly is penalizing you unless you forcibly take undue risks which are the employer's responsibility to address.