Hi Mydreamw,
You don't need to have an account with ICICI or any bank to have an salary account. However the are few eligible criteria (ICICI) which the company has to have. They are,
1. The organization/company needs to have a minimum of 20 employees employed within.
2. The total annual payout for the employees should not be less than 36,00,000/- INR.
3. 15,000/- INR should be the average salary, paid every year.
Also please be advised that you don't need a introducer/introduction to open a salary account.
In your case, I don't think so you would be able to open a salary account with any bank, until your employee strength becomes 20. As our fellow member Bhaskar said you shall pay them through cheque, which is as well accounted and would be useful in Du-delligence/Audit.