IMO this is more of a personal preference and comfortability thing. I personally would have my handyman do it or hire a contractor on my own to go in and do the work. I have a few tenants that do small basic tasks at the properties, I trust their ability to do so and do the work correctly but that it typically tasks such as unclog drains, replace leaky faucets and things of that nature. They do the work in their unit and submit the receipt for parts and I reimburse them for the parts. Again I trust these few tenants and their ability.
I will say though that you do own the HVAC system and it would be in your best interest to do the recommended upkeep and maintenance on it and it should be your responsibility to pay for such repairs/maintenance. It should not be the tenants responsibility to pay for or complete upkeep tasks on your property unless they want things done more than the recommended frequency by the manufacturer of the product.
If the manufacturer suggests the filter should be changed twice a year but the tenant wants it done every 3 months than you explain to them that per the recommendation of the manufacturer I replace the filters every 6 months however if you would like to have it done every 3 months than you are more than welcome to have that done the extra 2 times per year at their expense but they must use your contractor as only they are authorized to perform work on HVAC systems in properties you own and ask them to submit a copy of the invoice after it is completed for the record of the property. But don't use that to avoid having it done regardless the two times per year that you would normally.
