Here is the simplest thing that could work, I think. Try this out in your workbook or some equivalent place to make sure it does what you want.
Create a new node, named perhaps "Insert Time in Head". Put the following into the body:
p.h = ''
c.k.simulateCommand('insert-headline-time')
(There may be other ways to activate a Leo command, but this is the one I know about).
Select this node and press the script-button key to make a button for this command. Now create another new node, and press your new button. The new node's headline should change to the date, e.g., "4/22".
After you play with this and decide it does what you want, you can move the command over to MyLeoSettings.leo so that it will be available to all outlines. If you like it as a button, copy the node to the @settings/@buttons subtree, and change the node headline to @button
Insert Time in Head.
If you want a command but not a button, put its node into the @settings/@commands subtree, and change the node headline to read @command Insert Time in Head.
If you'd like this command to have a keyboard shortcut, add one to the node's headline:
@command Insert Time in Head @key=Alt-F9.
After you restart Leo, your new command will be available to every outline.