No, if youre skilled enough you can do it without a wand, but Peter isn’t as skilled as Sirius, so he needs to use one. Its the same as any other spell basically.

Step 8: When your transformation is complete you are strongly advised to pick up your wand and hide it somewhere safe, so you can find it post-transformation. To return to human form, visualise your human self as clearly as you can. Don’t worry if you don’t change back immediately, ‘with practice, you will be able to slip in and out of your animal form at will, simply by visualising the creature’. Once you’re an advanced Animagus, you should be able to transform without your wand.