First of all, many thanks to my co-worker Matt Wittemann (also BLOGging on www.askdynamicscrm.com) for providing the answer to this one.

So here's the code for removing a single item from a picklist in Microsoft Dynamics CRM 4.0 using JavaScript:

 

crmForm.all.customertypecode.DeleteOption(1);

 

Yep, that's pretty much all that there is to it.  I'm embarassed to say how long I played around and experimented with this - before I got an answer in about 30 seconds from Matt.  Thanks Matt.