I do not believe Photoshop allows users to use modifier keys for Tool shortcuts, any modifier, not merely the Shift key.

The Shift key won't present the warning above, it'll merely be ignored. The Shift key already plays an important roll in tool shortcuts within Photoshop.

Much like Illustrator, using Shift with a tool shortcut in Photoshop cycles through tools in a set.

For example, typing b selects the Brush Tool. Then typing Shift+b selects the next tool in the "brush" tool group - the Pencil tool, typing Shift+b again selects the next tool - the Color Replacement Tool, etc.

The problem with the Pen tool group is seemingly, by default, Shift will only toggle/cycle between the Pen Tool and the Freeform Pen Tool. It doesn't go any further into that group (at least here).

But, you can change that. Rather than inserting a new shortcut, merely add the existing Pen Tool shortcut for the other pen tools. The Shift cycling only works if the shortcut is set the same as the other tool shortcuts in that particular tool group.

So, if you set the Convert Anchor Tool shortcut to P to match the other Pen tools, then you can cycle to the Convert Anchor Tool by using Shift+P.
^{(You could change them all to C but then you lose the Crop Tool group shortcuts)}

Note this also allows you to control the Shift cycling. If you remove one of the shrotcuts, it'll no longer be cycled to with the Shift shortcut. So, for example, I never use the Freeform Pen Tool. By default the Freeform Pen Tool has the P shortcut so it shows up when cycling through the tool with the Shift key. If I remove the P shortcut for it, it will no longer be part of the Shift cycling.

I do not believe Photoshop allows users to use modifier keys for Tool shortcuts, any modifier, not merely the Shift key.

The Shift key won't present the warning above, it'll merely be ignored. The Shift key already plays an important roll in tool shortcuts within Photoshop.

Much like Illustrator, using Shift with a tool shortcut in Photoshop cycles through tools in a set.

For example, typing b selects the Brush Tool. Then typing Shift+b selects the next tool in the "brush" tool group - the Pencil tool, typing Shift+b again selects the next tool - the Color Replacement Tool, etc.

The problem with the Pen tool group is seemingly, by default, Shift will only toggle/cycle between the Pen Tool and the Freeform Pen Tool. It doesn't go any further into that group (at least here).

But, you can change that. Rather than inserting a new shortcut, merely add the existing Pen Tool shortcut for the other pen tools. The Shift cycling only works if the shortcut is set the same as the other tool shortcuts in that particular tool group.

So, if you set the Convert Anchor Tool shortcut to P to match the other Pen tools, then you can cycle to the Convert Anchor Tool by using Shift+P.
^{(You could change them all to C but then you lose the Crop Tool group shortcuts)}

Note this also allows you to control the Shift cycling. If you remove one of the shortcuts from a tool, that tool will no longer be cycled to with the Shift shortcut. So, for example, I never use the Freeform Pen Tool. By default the Freeform Pen Tool has the P shortcut so it shows up when cycling through the Pen Tool group with the Shift key. If I remove the P shortcut for it, it will no longer be part of the Shift cycling.