You don't really need access to change MX records.. unless you want to redirect incoming mail..
All you need is to change the line saying
www A IP ADDRESS
so that "IP ADDRESS" is the IP Address of your server. Then just setup your server to answer for the particular domain you've set up. You don't necessarily need to use DNS, if your registrar allows you to change the DNS records like detailed above.
If they don't, then they will for sure allow you to change nameserver addresses, then that's a different story.. You will need to setup DNS on your server, but that shouldn't be too hard to do anyway!
You will have to contact your registrar and ask him to update the MX records for your domain. You will have to change the WWW and A record and point them to the IP address for your server which will point the domain to your server.