Well, what you really need (in the pic) is called the plunger. The solenoid is the part with the electric windings that, when energized, draws the plunger into it to activate the choke linkage.
If you can't find a used one, either on eBay Motors or from a parts motor on your local Craigslist, you may able to get one from a Merc dlr.
Here's a good place to look up parts numbers for your motor:
http://www.mercruiserparts.com/selectDocs.asp?doc_nbr=83778
The part you're looking for is called "PLUNGER AND LINK ASSEMBLY, CHOKE SOLENOID" on this diagram:
http://www.mercruiserparts.com/Show...9&bdesc=CARBURETOR+LINKAGE+AND+CHOKE+SOLENOID
Part # 90548A1 (old part # 54283A1) which shows as NLA, but some dealers are likely to have a few NOS parts kicking around, so it'd be worth making some inquiries.
HTH and have a happy holiday season...........ed