Save a user field without calling hook_user_update
field_attach_update() may do what you need

https://api.drupal.org/api/drupal/modules%21field%21field.attach.inc/function/field_attach_update/7

A comment on the API doc page mentions using it to update a node's fields without updating the node.

If your custom field isn't part of the user object, you may just need to use drupal_write_record to write your field data.