In case the snapshot model of VirtualBox is not sufficient it is possible to enable a special mode which makes it possible to reconfigure storage attachments while the VM is paused. The user has to make sure that the disk data stays consistent to the guest because unlike with hotplugging the guest is not informed about detached or newly attached media.
The expert storage management mode can be enabled per VM executing:
VBoxManage setextradata "VM name" "VBoxInternal2/SilentReconfigureWhilePaused" 1
Storage attachments can be reconfigured while the VM is paused afterwards using:
VBoxManage storageattach ...