If you are planning to use the claymore all the time, I'd suggest finding a better defensive skill to major in. Heavy Armor, for example. Majoring Block will improve the damage you knock off of an enemy's attack, but as you said, the vast majority of the perks require a shield.
I'm with him. ^^
Whilst 2h block can do similar blocking to a shield, it is ultimately much weaker as the levels progress. The type of tank-character you would need to wield a claymore/2h axe will by neccsity have high Endurance/Strength stats and thus be better suited to Heavy Armour skills. The HArmour will protect you from an errant hits you take during the heavy combat.
During battle, do block still using 2h weapons, but don't invest in the skill. That slot could be taken up by something better like Heavy Armour, Armour Repair, Blunt, Blade etc. You may even want to put Athletics in to help get your presumably weighty and slow character moving around a bit. During battles especially on the planes of Oblivion, your tank character can very easily get surrounded and may need some extra speed to whip around and attack quickly.
http://www.uesp.net/wiki/Oblivion:Skills
This page shows you want I mean. See how athletics is within the category of "Combat"? if you are not going to use Block, you will need to choose a skill from either Stealth or Magic to complete the 7 skills.
As the diagram shows, each arch-type of Combat, Magic and Stealth has exactly seven skills that pertain to it - with Block absent, I reccommend choosing Destruction, as that will allow your character to lash out with some fire or such in times of need.
I hope that helps in choosing your skills!