Do I need to charge my Swiss clients VAT?

To be honest your posting is not very clear on several details. So you cover something as complicated as this, read the following, remember it is not legal advice.
In general you do not have too. I expect you will need some documents to clear that hurdle. However, I am no gestoría. I doubt if you will encounter one on this forum. You should seek advise from one.
If you run a business in Spain then you will have a tax gestoría to help you with returns of tax information. What do they say?
Please let us know as it would help with the knowledge base of this forum.