You'll almost certainly need to change the ECM (Engine Control Module) in your '87 Chevy after swapping a 350 for a 305. The 305 and 350 have different fuel injection systems, firing orders, and potentially different sensor configurations. The original ECM programmed for the 305 won't be able to correctly control the 350's fuel delivery, ignition timing, and other vital functions. Trying to run it with the original ECM will likely result in poor performance, running problems, or even damage to the engine.
You'll need an ECM programmed for a similar-year 350 TBI (Throttle Body Injection) setup, or possibly a programmable aftermarket ECM to get it running properly. A used ECM from a similar-year, similar-equipped vehicle is often a cost-effective option, but you must ensure it matches your specific setup (automatic or manual transmission, etc.). A completely custom tuned aftermarket ECM offers more flexibility, but is more expensive.