He'd probably gone up to the light, so The Shadow continued his climb.
The Shadow would continue that part, unless circumstances demanded otherwise.
Taking the turn in the passage, The Shadow continued his progress.
The Shadow continued to use his compass as a check on the radio beam.
The Shadow continued to the ground floor, intending to interview the inventor.
The Shadow continued through the darkness at a more reasonable pace.
"There was at least one other page," continued The Shadow.
Within the office, the door closed behind him, The Shadow continued until he came upon a strong safe in the corner.
The Shadow continued the chase; halfway to the corner he ran into trouble.
Then there was darkness again, and the disguised Shadow continued to wait.