To add Skype buttons in an listing, you need to check the following:
1. Skype is supported under all the categories of the listing, and on the site on which you are adding the listing. You can use GetCategoryFeatures API to determine if these prerequisites are satisfied for the category of interest.
2. The seller has a Skype account and has linked it (on the eBay site) with his or her eBay account. In production, if no SkypeID is linked to the AddItem requester ( a seller), the AddItem will be completed with a Warning 2190835 'Skype name does not exist'.
To fix this, you just need to link your SkypeID/s to your eBay sellers account as described here .
NOTE. Since linking a Skype account to one's eBay account is not supported in Sandbox so that you can't add Skype buttons in your listing in Sandbox.