Pairing Apple Watch to new iPhone without erasing
The watch backs up periodically, but you can’t easily get at the backups until you bring an unpaired watch to the phone containing the backups. 

I don’t foresee this changing this fall 2019 but a cloud backup interface would be needed to do what you ask if the watch or another wearable was to stand without the iPhone to manage data and setup. 

I’ve not seen any way to jailbreak a watch and repair it either which is what you’re looking to accomplish so until new information comes to light, you’re stuck with only one option. 


Get an iPhone to recover whatever backup exists of the lost iPhone, then wipe the watch and repair. You certainly want to engage apple support in case they have any insight into how they plan to handle this situation or if we don’t know enough and there are other options.