I don't believe any such command or key exists, but you could probably do this with scripts. A script for each type of movement you want, then bind it to an icon and finally to a keyboard shortcut of your choosing.
This zip folder contains several scripts that allow you to traverse the layers palette. First a quick description of each so you can decide which ones you want to use.
- SelectNextLayer - This selects the next layer in order. Including going in and out of layer groups.
- SelectPrevLayer - This selects the previous layer in order. Including going in and out of layer groups.
- SelectNextSibling - This selects the next layer in order but doesn't go in or out of a layer group. If you're in a layer group it'll only select the next layer inside that group never leaving it. Or if you're outside of a layer group it'll never select any of the layers inside the layer group
- SelectPrevSibling - Same as above just down instead of up.
- SelectBottomLayer - Selects the bottom most layer of the layers palette, escaping layer groups.
- SelectTopLayer - Selects the top most layer of the layers palette, escaping layer groups
- SelectFirstLayerInGroup - This will select the bottom-most layer inside of a layer group if you're inside the group already, or have the layer group itself selected, going into the group.
- SelectLastLayerInGroup - This will select the top-most layer inside of a layer gropu if you're inside the group already, or have the layer group itself selected, going into the group
To Bind these to shortcut keys
1) Unzip the scripts into your Scripts-Restricted Folder
2) Inside PSP go to View -> Customize
3) Select the "Scripts" tab.
4) In the scripts tab, select the script you want to bind, select an icon for it, and then click the "Bind" button. Bound scripts will appear in the bottom list
5) Repeat until you have all of the scripts you want bound.
Bound scripts can be added to menus, context menus, toolbars (including the layers palette toolbars), and keyboard shortcut keys which is what we'll do next.
Now that you have the scripts bound I recommend closing the Customize dialog and re-opening it. It'll make the next step easier, but if you don't want to you don't have to.
1) If you closed Customize dialog, re-open it.
2) Select the "Keyboard" tab
3) From the category choose "Bound scripts" if you don't see "Bound Scripts" you probably didn't close the Customize dialog. So choose "All Commands" instead.
4) Find the script name you want to add a keyboard shortcut to.
5) click inside of the "Press new shortcut key" text box.
6) Press the shortcut key you want to use, it will show "[Unassigned" if the key is free to use. Or it'll tell you which command that key is already attached to.
For example Ctrl + J is unassinged, while Ctrl + M is assigned to "Flip Horizontal". You can unassign keys from current commands if you want to switch things up.
7) Once you have a key combo you like, hit the "Assign" button to assign it.

Once you're done, close the Customize dialog.
Your keyboard shortcuts should now work.
You do not have the required permissions to view the files attached to this post.