Hi,
if "site-2-site" LAN means VPN (IPsec static tunnel) then the answer is yes, you must switch to routed mode.
There is no VPN in transparent mode.
When switching to routed mode the asa will always reboot and come up with an empty config.
So I'm afraid you will either need some help on the side of the data center .
E.g. an engineer at the datacenter could connect to the asa physical console and permit you to use some desktop-sharing like team-viewer for an initial config: ip address, no shut, routing, rsa-keys and ssh-setup. I did it a couple of times recently and it worked prettty fine.
Otherwise you will need to be there physically.
Rgds, MiKa