Without downtime is not possible to migrate live servers without vCenter.
If you don't have much changes on the virtual machine, then you could use ghettoVCB shell script(it is a free backup solution) to create snapshot of the live running machine to the other ESXi server. (I assume you have shared storage already which is accessible from both ESXi host)
Then you could bring up the newly created copy on the other ESXi server.
But this involves a loads of manual implementation via ssh in the source server. (upload the script, edit the destination drive, make the script executable for the system, etc-etc...)
But with this, you can switch from one live server to the other at relatively small downtime. Switching off the virtual machine's network access from the source server and switching it on, on the destination ESXi host. (takes less than 30 sec)
I used this quite several times and worked just fine.
After all the vCenter does the same thing automatically when you migrate a live machine. :)
Please check the backup script here: https://communities.vmware.com/docs/DOC-8760