I spoke too-quickly regarding the radioactive shielding requirements, they're more manageable than I thought [1]. For the 10-cm thick tungsten wall, following [1], it looks like the shielding factor is ~25,000. That's more significant than it sounds, because only the gammas emitted at the surface of the cobalt see that shielding factor. The rest are better shielded, up to factors of 10^11 in the best case (propagating all the way across the sphere).
It's still a spooky thing to assemble, but it does appear that if the shielding is preserved, that it could be done without ridiculous quantities of assembly/launch shielding.
A 30cm sphere has a volume of around 1.1 x 10^5 cm^3. Cobalt's density is about 8.9g/cm^3, so we're looking at roughly 10^6 grams of 60Co, or about a ton of the stuff.
60Co puts out 1100 Curies of radiation per gram, so this sphere represents about 1.1 billion Curies. To put this in perspective, a nuclear weapon detonation releases on the order of 1-5 MCuries of fallout: the Chernobyl disaster vented about 200 MCuries into the environment: total contamination left behind by the Soviet nuclear weapons program is estimated at around 3 GCuries.
I am not sanguine about a research experiment that requires assembling multiple Chernobyl's worth of high level gamma emitters in a red-hot capsule, dropping it on the ground, and hoping it stays intact ...
It's still a spooky thing to assemble, but it does appear that if the shielding is preserved, that it could be done without ridiculous quantities of assembly/launch shielding.