Link Skype to Alexa on a per-device basis
You'll need to work with Amazon on this but, please find a way to link Skype to Alexa on a per-device basis.
My sister and I bought an Echo dot for our mother in Pennsylvania. Sister has it set up under her Amazon account for ease of configuration. Mom doesn;t have a smart phone or a computer and has zero interest in configuring an Echo,
We also set up Skype fr Mom, but I can't call Mom on her Echo with Skype bcause it will ring in my sister's house, 2500 miles away.