Update if possible. The security in the latest version is much improved. If you are using IWP you will need to work around how you do that in Web Direct or CWP.
Safe Yes, but FileMaker Inc is not supporting the version anymore so big chance that you might run into problems. Much better to update to FileMaker 15 that is a very good version of FileMaker.
You may want to limit access to the server to go through a VPN and not expose it to the public internet.
Of course you can use an older version, but in case you run into a security problem, OS compatibly problem or a non working function, everyone will just suggest moving to the newest version.
the database would be hosted on an external server, but only available to those that have the link and password. I asked a filemaker developer to do some adjustments to the database and he actually refused. He said if I update he is happy to help, but that he can't support a project were data security isn't observed enough...
You should detedrmine if your external server or hosting company can work with FM11 format files.
FMP v 7 to FMP v 11 the file extension was .fm7.
From version 12 till now the file extension is .fmp12.
FMserver 11 can not host .fmp12 files and fm server 12/13/14/15 can not host .fp7 files.
I would be interested in the work so PM me.