“Jersey Shore” star Nicole “Snooki” Polizzi declared she is cancer-free seven months after receiving a Stage 1 cervical cancer diagnosis. “As of right now, I am cancer-free,” she told People Friday, adding that she feels like she’s “on the other side” following a successful hysterectomy in July. “They got everything out. So I’m definitely happy that I did it.” The reality star admitted she “avoided getting [a] pap smear for a long time” before she finally received the scary diagnosis. “And once I finally went to the doctors, I feel like it’s just been week after week of doing a procedure, then another procedure, and then a hysterectomy. So…