Wouter, I agree with James. By definition, shared hosting environments tend to have more things locked down, since they are sharing a server with multiple clients. Since you don't have unfettered access to the server, you would need to work closely with someone at the shared hosting company to verify the requirements and permissions.
A fairly cost effective alternative (to shared hosting) would be to get a small AWS Windows virtual machine and host your web app and SQL Server database there. Then you would have full access to the machine and full control over the application.