If your team is using both Slack and Skype, I think it'd be better to choose a tool and stick to it. Face-to-face communications can still happen via video for both tools, so you can still have that but it may just require more coordination and isn't as instant as in the office.
As your team slowly gets a hang of things, another thing I'd keep in mind is to make sure you keep the team motivated and maintain a good remote team culture, as remote work may feel lonely at times or team members may feel detached from one another.
There are some well-known remote teams that you can try to learn from, like Buffer and Zapier.