Using this extension customer will checkout only with your store default currency but they can use currency conversion feature(select box) too only for viewing purpose

Installation

1. Go to o your store admin panel. Navigate to Extensions -> Extension installer.
2. Click on the upload button. A dialog box should open.
3. Locate the installation file of this extension(checkout_default_currency.ocmod.zip) and select it.
4. Now this module should be visible in Extensions -> Modules.
    After locating it in the Module list just click the install button (“ + ” sign)
   Then edit this installed module and enable it from there.
5. Go to Extensions -> Modifications and click the Refresh sign at the upper right corner of the page.
6. Done. Now customer will checkout with your store currency.