Yes it should be possible to connect without a router.
You can try to use the ad hoc network (sometimes called a peer to peer network) in your computer using the network set up wizard. Then try to join the ad hoc network from your printer's control panel.
These are Kodak's instructions:
When connecting to an ad-hoc network, a reset of the Wi-Fi radio may be required to accept the ad-hoc Auto-IP (link local) IP address. Turn the power to the printer off and then back on. Review your network settings after the printer is turned on again. We recommend that you set up a static IP address on the printer for your ad-hoc wireless network connections. Assign your own IP using the 255.255.0.0 subnet mask.
The printer can only join an existing ad-hoc network. Your printer does not support creating an ad-hoc network through the control panel. You must use your computer to set up ad-hoc networks. You should not choose Manual IP address when in ad-hoc mode. You should instead use the WiFi Setup Wizard to join another network.