I am in Karelia with a couple of infantry and tanks. The german territories are heavily fortified. I don't want to lose what few units I have. Do I have to conduct combat or can I skip to noncombat move phase?
You can opt not to move units in the combat move phase. However, you have to declare all your combat movement and carry it to resolution before doing non-combat stuff. So you can't, say, non-combat-move reinforcements out of Moscow into Karelia and then declare an attack using eastern troops against something Japanese.
It's tempting to want to deal with the stuff you find "most important" first to get it out of the way, but your combat stuff is the most important stuff. :) So look at all your troops and determine all your attacks first. THEN, if you don't have any combat moves you want to make, move to the next phase of the turn.