If this is your only card and already reported to CIBIL, then CIBIL score may go down if you close it.
If you have other cards older than this one, that are getting reported to CIBIL, then the score would not decrease.
You can try their score simulator as well.
If new card is not reported yet to CIBIL, then no worries.
On the variant front, you could still ask them to change the card network. They can't deny if the same card is available with other network as well.