How to remove other apps icons (like Skype or WhatsApp) from contact and phone app?
go to Settings > Accouts and choose Skype/WhatsApp > then search for each one how do you remove the sync contacts. After this your Contacts list should update not showing Skype/WhatsApp data.

As for the call using skype, you should have the option to choose Phone and click Use Always.

This is very phone dependent, so if you cannot find this options, tell us more about your phone and Android version.