Black Shadow spent his time just thinking of what decision he should make. Kelsy told him that there was a time limit before he would meet his end. He had to admit that Kelsy's proposal was tempting.
If he was still the Black Shadow before then he won't have a second thought and would accept her offer right away just to save his life. Loyalty and friendship were not in his vocabulary before. But everything changed. Just like Catseye, he was a changed man now.
If he talked then the whole organization would be put in danger. Even if he would lie to them, he knew that it was just a matter of time before the Dark Lord and Dark Knight would learn about it. Instant death was waiting for him.
He was still wounded so he had no ability to escape this place as of this moment. So accepting Kelsy's proposal and saying some lies or false information to them was not a good choice. It's just delaying his time of death but in the end, his ending would still be the same.