What kind of action is it to put away a shield without dropping it?

I am currently playing a sword and board slayer how likes to switch his warhammer to two-handed or back in a pinch.

However, it is not clear to me how I can do this without dropping the shield. He is currently using a heavy shield.

Case 1: Warhammer two-handed, switching to one-handed use and equiping the shield

Case 2: Warhammer and Shield in hand, switching to two-handed use while putting away the shield without dropping it

Case 1 seemed clear at first:

FAQ

Two-Handed Weapons: What kind of action is it to remove your hand from a two-handed weapon or re-grab it with both hands? Both are free actions. For example, a wizard wielding a quarterstaff can let go of the weapon with one hand as a free action, cast a spell as a standard action, and grasp the weapon again with that hand as a free action; this means the wizard is still able to make attacks of opportunity with the weapon (which requires using two hands). As with any free action, the GM may decide a reasonable limit to how many times per round you can release and re-grasp the weapon (one release and re-grasp per round is fair).

So switching from two-handed grip to one-handed grip with a one-handed weapons should also be a free action.

Ready or Drop a Shield

Strapping a shield to your arm to gain its shield bonus to your AC, or unstrapping and dropping a shield so you can use your shield hand for another purpose, requires a move action. If you have a base attack bonus of +1 or higher, you can ready or drop a shield as a free action combined with a regular move. Dropping a carried (but not worn) shield is a free action.

So if have my shield on me, say over my shoulder, I take a free action to switch my grip to one-handed, a move action to ready my shield, an I have standard action left to attack.

Is that right?

Case 2: There is no mention of putting away or stowing a shield as far as I can see. So I have to look elsewhere.

Draw or Sheathe a Weapon

Drawing a weapon so that you can use it in combat, or putting it away so that you have a free hand, requires a move action. This action also applies to weapon-like objects carried in easy reach, such as wands. If your weapon or weapon-like object is stored in a pack or otherwise out of easy reach, treat this action as retrieving a stored item.

Is a shield a weapon-like object? It would be carried in easy reach, over the shoulder or on a hook somewhere I suppose. A shield can be a weapon if using a shield bash. That would make it a move action to put the shield away, free action to switch grips, which leaves a standard action to attack.

Manipulate an Item

Moving or manipulating an item is usually a move action. This includes retrieving or putting away a stored item, picking up an item, moving a heavy object, and opening a door. Examples of this kind of action, along with whether they incur an attack of opportunity, are given in Table: Actions in Combat.

Or do I have to take a move action to unstrap (without the dropping part) and another move action to put away an item? That would mean, that I couldn’t attack. So it would be quite important to know how it’s done right. This might also mean for Case 1, that I first need to retrieve the "stored" shield with a move action, and then ready it with another mode action.

Now I looked at the quickdraw shield:

Quickdraw Shield

If you have a base attack bonus of +1 or higher, you may don or put away a quickdraw shield as a swift action combined with a regular move. If you have the Two-Weapon Fighting feat, you can draw a light or one-handed weapon with one hand and a quickdraw shield with the other in the time it would normally take you to draw one weapon. If you have the Quick Draw feat, you may don or put away a quickdraw shield as a free action.

Finally a mention of putting away a shield, no drop required. However, it talks about donning the shield which takes me to the armor and shield section.

Getting into and out of armor

Don: This column tells how long it takes a character to put the armor on. (One minute is 10 rounds.) Readying (strapping on) a shield is only a move action.

Remove: This column tells how long it takes to get the armor off. Removing a shield from the arm and dropping it is only a move action.

So donning seems to equal readying.

Does this mean, that the only way to put away a shield is to use a quickdraw shield (which might be a good idea anyway), or is there something I missed? Do I need two move actions and cannot attack in the round in which I switch from sword-and-board to two-handed?

Thanks in advance!