DES decryption of the homomorphic encryption ciphertext

I implemented an application using partial homomorphic encryption for outsourced computations. To get an efficient bandwidth, I am thinking to apply (DES) symmetric algorithm to encrypt the message instead of HE before uploading it to the cloud.

Can I perform DES decryption operations (permutation and S-boxes) on homomorphic encryption ciphertext?

$
begin{align}
&C = operatorname{DES}(m)\
&C’= operatorname{FHE}(C) = operatorname{FHE}(operatorname{DES}(m)) \
&operatorname{DES}^{-1} (C’ )= operatorname{DES}^{-1} (operatorname{FHE}(C))= operatorname{DES}^{-1} (operatorname{FHE}(operatorname{DES}(m)))= operatorname{FHE}(m)
end{align}
$