Mung Bean Nuclease would ligate ssDNA, but not the blunt dsDNA parts.
But you may look in the whole Nuclease section on NEB site, if you find some more suitable, from what I was looking BAL-31 nuclease looks interesting. But it will also cleave at nicks within your circular dsDNA.
But I would be a bit affraid that crosslinking may cause some damage to the strand enough to be a template for a nuclease.
If the complexes are bigger and circular, it's probably better to use purification/isolation protocol, that will degrade and wash out the smaller non-circular dsDNA and other fragments.