Unpairing watch from old iPhone without computer

You can unpair the Apple Watch from the iPhone without the iPhone nearby.

Have a look at the second part of this related article:

Unpair and erase your Apple Watch - Apple Support

You can also remove the Activation Lock in iCloud:

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If you can't access your iPhone or Apple Watch, or if your Apple Watch isn't paired with your iPhone and you need to turn off Activation Lock:

1. Go to iCloud.com and sign in with your Apple ID. 
2. From the Quick Access Menu in the top right, select Find My. You might be required to sign in.
3. Select All Devices, then click your Apple Watch.
4. Click Erase Apple Watch. Select Next until the device is erased.
5. Click the remove button next to your Apple Watch.

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copied from: About Activation Lock - Apple Support