Switching the conversation to any other device will keep the messages you send tied to the earlier device used for chatting, meaning the chats encrypted will not be transferred to another device if the chat is with the same person. If they do not accept before then, the invite will expire, and you will need to send another one. With end-to-end encryption, the contents of messages can only be read by the sender and recipient and will not just be sitting on Microsoft's servers. You can do that by right-clicking on the conversation and selecting Delete chat. This means that Skype users may see a complete roll out of end-to-end encryption in the coming days if all goes well.
I thought I should also let you know that that the end-to-end encryption doesn't extend to video chats. Matching build versions between users is required to try out the feature. The messaging service will soon benefit from end-to-end encryption, something that its rivals, WhatsApp and Messenger already offer for quite some time. Microsoft has released this feature in the preview for Skype Insiders only. For now, all of these conversations must be one-to-one, as no group messages are allowed.
For the time being, Private Conversations are available for Insiders using Skype version 18.104.22.168 for iOS, Android, Linux, Mac, and Windows Desktop. According to a report from Der Spiegel-which itself references documents disclosed by Edward Snowden-sustained collection of Skype conversations became possible in February 2011, months before the chat app was acquired by Microsoft.