Your initial thinking is spot on. While we could add the link to a custom property with a field type of rich text, it won't render the player in the way you want. It will most likely just display a link to the external content.
A more likely solution is to leverage HubSpot UI Extensions. This section of the developer documentation shows that you can use this feature to customize the “middle column” of a record: Locations. I'd recommend starting there.
Please note, this is a moderately advanced solution and will require developer resources. To work on this safely, your team can create a free Developer Account, which allows for the creation of Developer Test accounts to build and test this functionality outside your production portal.
Have fun testing! — Jaycee
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