Is the share capital part of what I pay OCC for a Japanese company?

No. The package covers the set-up work and government fees. The capital is your company's own money: before registration it is paid into a designated bank account, often one held by a promoter or director, and the bank statement becomes evidence for the filing (confirm the account route with your specialist).

Japan company guide

Source: 1.3 Procedures for registering establishment, Japan External Trade Organization (JETRO)