If you are not the owner of the device (i.e., creator of the DHF), you are the private label manufacturer and both your company and the company in China will need device licenses in Canada. If you want to purse a manufacturer's license, you will need the design dossier essentially. For example, class II devices require a biennial post market summary report to be created and updated. In that report, you will need to assess the change in risk based upon customer complaints, adverse events, CAPAs, NCs, design changes, etc. You likely do not have all of this information if you are not manufacturing the device. Additionally, the report requires the creator to determine if there is a change to the established benefit-risk analysis based upon the post-market data analyzed during the reporting period. If you do not own the design of the device, you likely do not have the full risk file. If you are the private labeller, you do not have to complete this report; it is completed by the actual manufacturer.
Unless you can get the full device file from the manufacturer, you will need to apply as a private label manufacturer and get a private label class II device license. Your supplier will need a manufacturer class II device license and an MDSAP certificate.
Health Canada will not accept an ISO 13485 certificate unless it is to the CA/CSA version of the standard. You are probably better off going for MDSAP which has been required to apply for a medical device license since 2019. The guidance does look like it has provision for private label manufacturers to not have a ISO 13485 certificate, however your manufacturer in China will need an MDSAP certificate to obtain the device license to which you must link your private label device license. Either way, unless you have an MDSAP certificate, your company is still subject to inspections by Health Canada. They can inspect even with an MDSAP certificate in place, but these are usually for-cause inspections.
If you are causing the device to be labelled with your company's name, you fall under the definition of a manufacturer under Health Canada's rules even if you do not partake in any actual manufacturing activities.