How to verify a number encrypted with an unknown key
You probably don't need to re-encrypt using the Paillier crypto system.

1) Alice encrypts $c_1=g^{m_1} r_1^n$ und $c_2=g^{m_2} r_2^n$ and computes $r_3=r_1 \cdot r_2$ and $m_3=m_1+m_2$, then sends $c_1$, $c_2$, $m_3$ and $r_3$ to Bob

2) Bob computes $c_3=c_1 \cdot c_2=g^{m_3} r_3^n$ - If the homomorphically computed sum matches the re-encryption Bob will believe that $c_3$ encrypts $m_3$

The basic idea is that $g^{m_1} r_1^n \cdot g^{m_2} r_2^n = g^{m_1+m_2} (r_1 \cdot r_2)^n$

All cipher text operations are executed modulo $n^2$

This proof is backed up by Paillier's original paper.
Unfortunately the proof is not absolutely Zero Knowledge as the sum may give you information about the possible summands. However you may choose large similarly sized primes for the $r$s so an attacker would need an efficient solution for prime factorization (see other question here).