Yeah, I second that.
You'll want to have the mainsail to balance out the boat.
The boom is not that critical for these daysailers, in that it just needs to be the correct length for the foot of the mainsail (and in your case, to go behind the cockpit at the level of your traveller, and strong enough. You'll need to add a pulley on the end for your mainsheet, and an attachment point on it for the boomvang, and a pully and cleat for the outhaul. Then of course something to attach it to the goosneck.
If your mainsail slides into a grove, then it complicates things, otherwise, you could just find a nice aluminum tube of a reasonable diameter (or even make it out of a nice grade wood), and just add the above listed parts. You could easily pull one together for little or nothing with a little elbow grease, and in no time at all.
So yeah, don't spend too much, grab a boom of a similare length, cut it down as needed and add the missing bits. Should be a nice fun project