How do I create a secure encryption scheme using addition?
Your idea of addition modulo 10000 is correct.  The correctness follows from the fact that $\mathbb{Z}_{10000} = \{0, 1, \dots, 9999\}$ equipped with addition modulo $10000$ forms a (finite) group.

Let $m \in \mathbb{Z}_{10000}$ denotes a PIN code.  Now choose a uniformly random element $r \in \mathbb{Z}_{10000}$ and define $c = m + r \bmod 10000$.  It is easily seen that $c$ is a uniformly random element in $\mathbb{Z}_{10000}$.