The Pistol will always be with you no matter what you change, and will have unlimited ammo. There is no way to actually switch to your sidearm when playing; it is only equipped when you run out of ammo.
If you still haven't unlocked this by the end of the game, enter your armory and reset all of your unlocked items (Only if you haven't unlocked extra ammo clips). Choose the first gun that you have unlocked and start up one of the missions. This way you can easily run out ammo in order to use your pistol more during the level. Just make sure you don't shoot any ammo bonuses so you can keep your pistol out.