Even without making a wish, you still possess the powers of a Magical Girl including a Soul Gem. Your abilities are no longer reliant on your personality, wish, and other factors. This will be as if you made an imaginary wish, you can customize your Magical Girl outfit and weapon to suit your preferences.
Your unique magic is based on what you have decided on, be it from a replica of an existing Magical Girl or from something else and scaled to the Karma you possess. You can still make your wish at a later time, but whatever that wish might be you won't gain a new Magic, weapon, transformation, and so on.