If you are using Super Socializer or Sassy Social Share plugin for Social Sharing, you can follow the steps mentioned below to show Whatsapp icon only on mobile devices.

For Sassy Social Share plugin:

Add following CSS in the Custom CSS option in the Miscellaneous section at the plugin options page in the admin panel:
@media screen and (min-width:783px){a.heateor_sss_whatsapp{display:none!important}}
For Super Socializer plugin:

Add following CSS in the Custom CSS option at the Super Socializer > General Options page in the admin panel:
@media screen and (min-width:783px){a.the_champ_whatsapp{display:none!important}}
783px in the above code is the maximum width of the mobile device screen to show the Whatsapp icon. Screens wider than this won’t show Whatsapp icon. You can change it according to your needs.