The only issue with doing it that way is if it issues an IP of a device that already exists on the network it will be going on then you will run into an IP conflict.
You will need to know the scope in which the static IPs are set. Then on the DHCP network make sure it assigns an IP outside of the scope to not run into an IP conflict.
It sounds like the OP's original problem is now resolved, but just to round this out, let me spell out my previous suggestion in a little more detail:
1. Decide on the IP address that you wish the logger to have. (If there's no DHCP server on the network then presumably the user is in full control of the specific addresses they wish to use and can ensure uniqueness?)
2. Fire up the logger on a network that does have DHCP.
3. Identify the IP address that the logger has temporarily acquired (Weatherlink software or eg AngryIP) and open the logger's web interface in a browser.
4. Assign the preferred IP as a static IP (and gateway and subnet mask etc), double-check credentials and save back to the logger.
5. Return logger to primary network.
Is there some reason why this shouldn't work?