It’s up to you to decide to be suspicious or not, but the fact of the matter is that Dragonsreach can only hold one dragon at a time, and Odahviing is offering you your only method of travel to reach Skuldafn.  If you are reasonable he compliments you on your sensibility, but either way you’re going to have to free him.

Thankfully, when you pull the chain upstairs to release him from the stocks, he simply heads to the edge of the balcony and waits there- he’s a dragon, the things he should be doing will very well wait for him dammit, so he’s perfectly fine with waiting for you as long as it takes to get ready.

Before talking to Odahviing again, you will need to make absolutely sure you are ready.  Keep in mind that this is a trip for one, so you’re not going to have any followers with you.  In light of that, you’ll want to have as little in your inventory as possible in case of loot, but as much as you can gather in terms of potions and temporary-benefit items.  You’ll also want to make sure your level is high enough- Skuldafn is full of powerful enemies, and Alduin himself is very distinctly not a slouch.

Once you’re geared and prepared, return to the balcony and speak to Odahviing.  He’ll ask if you’re ready- to which you agree.  You then mount up just behind his head, and off you go into the sky.

Ohdaviing lands after a quick loading screen, dropping you off at the base of a large temple- this is Skuldafn.  Almost immediately, you’ll be assaulted by a fire-breathing dragon, as well as a few Draugr- the corpses are quick to take out, so handle any that are getting irritating before turning your attention to the wyrm.  Once you fell that, another one, this time belching frost, assaults you.  That’s all in the way of dragons for now, though.  You’ll continue encountering Draugr as you muck about the ruins, particuarly a large number of Wights who will pitch ice spikes at you and Overlords who will try to blast you away with their Force Thu’um.  If your level is around 30 or so, you can usually power your way through these by chugging stamina and/or magicka potions as well as downing a few bowls of stew.

Presently, you reach a gate.  This leads inside the temple, which bars your way with not only more Draugr, but also an occasional Nordic symbol-gate.  Pay attention to the walls for the depictions of creatures so you can correctly aim the symbol plinths, and this shouldn’t be too hard.  You’re rarely going to face enough Draugr at once to really drain your resources, so don’t worry too much about that- focus on problem-solving and grabbing the occasional high-end potion from the local loot.

Eventually you reach another claw-operated door, and guarding it is one last Draugr Overlord- who happens to be holding the very Diamond Claw you need to solve and open it.  Inspect the claw for the solution (Wolf, Dragonfly, Dragon in order from top to bottom) and open the door up.