Batch swap cache files in Constraints

We have a small script that swaps cache modifiers of one Alembic to Another:

import bpy

#look for cach file
if "Mesh Sequence Cache" in bpy.context.active_object.modifiers.keys():
    cache_file = bpy.context.active_object.modifiers['Mesh Sequence Cache'].cache_file
    cache_file = None

#assign cache file
if cache_file is not None:
    for obj in bpy.context.selected_objects:
        if "Mesh Sequence Cache" in obj.modifiers.keys():
            obj.modifiers['Mesh Sequence Cache'].cache_file = cache_file

How Can I do the same for constraints?