Dear Simmi,
First, let me tell you that there is no law that exists in India by which the management is bound to give sick leave.
Second, the mention of sick leave is there in Model Standing Orders under The Industrial Employment Standing Orders Act, 1948. Hence, if the Act is applicable to your organization, then you can refer to either the Model Standing Orders or your organization's Certified Standing Orders.
Even in the case of ESI, the ESIC pays for absence due to illness, and not the employer.
As for whether it is possible to give annual vacation in place of sick leave:
1. The two are different things, and since you are not bound to give sick leave, you need not think of it as an alternative to Annual Leave.
2. Your annual leave should be equal to or more than your statutory limit, i.e., Factories Act or Shops and Establishment Act, Plantation Labour Act as applicable.
If you maintain the above, you need not give separate sick leave unless there is a specific state rule to that effect.
Warm Regards,
SC