If you are using the external mail server like google,yahoo etc and you want to change the MX record for the domain than no need to contact your hosting provider as cPanel provide the option to the change the MX record from the cPanel.Its depend on the privilege provided your hosting account provider to your hosting account. You can refer the following steps to change the MX records.
In order to edit a MX record, login in the cPanel and first click on the “Mail icon” on the main menu of cPanel. Next, click on the Modify Mail Exchanger (MX Entry) icon. Click the Change an MX Entry link, and enter the domain of the new MX entry in the blank field. Click on the Change button.If you have any issue than refer the Video Tutorial