If the product involve at least two devices, one sitting at home as server and one you carry as client, then the IP should be your home IP.
If instead you want to hide your home IP, then just any regular VPN service (or hosting your own on a VPS) can work with a travel router that support built-in VPN client.
And yes, the company can notice that your IP belong to a data center if you use the latter option, they can also notice the much higher latency, use the tracking software to see your real location through nearby wifi & bluetooth (even if you don’t connect to them) etc
Could you share the link to the product? Generally, a VPN will achieve what you want. The client (your phone, laptop, etc.) connects through a server (at your home, in a datacenter, etc.) and thus connected from the IP of the server. So when connected to the VPN, your laptop shows as being at home when browsing google.com, for instance.
Now a “VPN travel router” could mean a few things… that’s why I say post the product. Very likely, it’s a standard router, maybe with a built in cellular modem, that acts as a VPN client to a remote VPN server, and then anything that connects to the router is behind this VPN.