Checkpoint will not flush pages from memory. Just writes dirty pages and they stay in memory, now in clean state. No danger there. Unlike lazy writer that responds to memory pressure and certain dbcc commands that really flushes-out pages from memory. You may benefit a little from that checkpoint step becase there is certain amount of time passed between implicit checkpoint that happens within tran log backup command and the shrink command. There could be benefit when log grows really fast, and log backup takes larger amount of time, but is not something essential. Just may give you a bit better result.

If you want to decrease number of VLFs, shrink to near zero, than expand to desired initial size in one step, eg 4000MB. Set the growth to fixed size as Gail said. Eg, 512MB or 256MB if your storage is not very fast. Initial size should be large enough to accomodate normal db operation without any growth.