Magento – How to Add Desktop Version and Mobile Version Link

The short answer here is no, though, you could drop a javascript cookie called forcedesktop and set it to true. This would be set onclick for the switcher link.

Then rewrite the design exception method to sniff for existence of the cookie:

app/code/local/YourCompany/YourModule/etc/config.xml

<?xml version="1.0"?>
<config>
    <modules>
        <YourCompany_YourModule>
             <version>0.1.0</version>
        </YourCompany_YourModule>
    </modules>
    <global>
        <models>
            <core>
                <rewrite>
                    <design_package>YourCompany_YourModule_Model_Design_Package</design_package>
                </rewrite>
            </core>
        </models>
    </global>
</config>

app/code/local/YourCompany/YourModule/Model/Design/Package.php

<?php

class YourCompany_YourModule_Model_Design_Package extends Mage_Core_Model_Design_Package
{

    protected function _checkUserAgentAgainstRegexps($regexpsConfigPath)
    {
        if(Mage::getModel('core/cookie')->get('forcedesktop')=='true'){
            return false;
        }

        parent::_checkUserAgentAgainstRegexps($regexpsConfigPath);
    }
}

Yes, what you looking for is a theme with "responsive design", which means the theme will change depending on the size of the screen.

If you google responsive design you will get some examples of it. There are alot of themes you get for magento that are responsive, but converting an existing custom theme to a responsive layout can be expensive

Updated due to original question being changed

If you do have a responsive design then you could use something like this:

http://filzhut.net/projects/responsive-switch/