This is possible without any downtime to the VM. However, as you are going to deploy new fresh vCenter again, you will have to configure HA/DRS settings again. Also, Since you do not have control on old vCenter, performance data from old vCenter you may not get as well. If you do not bother about performance data, you are good to go.
Here is how you can do this migration:
1. Deploy new vCenter: For your requirement : vCenter appliance will work just fine: Refer:http://www.virten.net/2013/09/vmware-vcenter-server-appliance-5-5-vcsa-limitations/
2.Create the cluster on new vCenter, configure the same. first add your new ESXi host 5.5 into cluster. Make sure shared storage on old ESXi host is visible on new host as well. If it is not possible, you can perform vMotion without shared storage as well. Refer:VMware vSphere 5.1
3. Now you can add your old host into new cluster, make sure vMotion requirement are configured already :
vSphere 5.5 Documentation Center
4. Add your old host to new cluster. once you add these ESXi host in new vCenter, both will be disconnected automatically from old vCenter. if your hosts CPUs are different, you will have to enable EVC: Make sure you understand impact of EVC, configuring the same.
Refer: VMware vSphere 5.1
VMware KB: Enhanced vMotion Compatibility (EVC) processor support
VMware KB: EVC and CPU Compatibility FAQ
VMware KB: Enabling EVC on a cluster when vCenter Server is running in a virtual machine
5. you can migrate your old host VMs to new host, once migration is over, you can keep your old host into maintenance mode, and remove the same.