No. The Canadian Charter of Rights and Freedoms is a set of laws that places limits on state action and prevents the state (provincial, federal etc.) from enacting laws that conflict with a particular set of constitutional values (e.g. freedom of expression, right to assemble, right to life and security of the person etc.). The Charter does not apply to employment relationships unless your employer is a state actor. Rather, employment relationships are governed by employment contracts and employment standards legislation.
The Nuremberg Code is a guideline developed after the trial of Nazi doctors for atrocities committed during World War II. It that says humans should not be subject to medical experiments without their consent. The Code does not apply because it is not enacted into Canadian law. Moreover, the vaccines available to Canadians are not experimental, rather they have been approved by Health Canada.
Employers are within their rights to establish vaccination policies. Where employees work with vulnerable populations or in close proximity to one another, employers can implement mandatory vaccination policies.