Why are you Vat exempt?
I suspect that you mean that you are not registered for VAT which is completely different.
If you are registered for VAT, you can provide your VAT number to the Swedish company and they should not charge you VAT.
If you have a VAT exemption certificate, which is unlikely, you can provide a copy to the Swedish company, and they should not charge you VAT.
If you are not registered and not exempt, they must charge you VAT.