Yes, you can do the static nat statement you mentioned. You will also want to create an access-list for the DMZ interface and allow the barracuda to communicate with your email server on what I'm assuming needs to be port 25.
If your barracuda IP was 172.16.1.10 and your Exchange server was 192.168.1.10 your rule would be something like this:
static (inside,dmz) 192.168.1.10 192.168.1.10 netmask 255.255.255.255
access-list DMZ_in extended permit tcp host 172.16.1.10 host 192.168.1.10 eq 25
access-group DMZ_in in interface dmz