I am entering into this debate late as I was not active on the site when you posted it. As it happens, this is a regular discussion in many of our client offices during audits.
First, I do not know why your client will be deciding or bothering about how you maintain your registers unless you are a contractor covered under the Contract Labour Act. In that case, you need to follow the requirements of the Contract Labour Act and not the Shop and Establishment Act.
All labor laws in India provide for the maintenance of registers. Though not specifically defined, it is understood that registers are manual and bound (sticker and bound actually) books in which the records are to be maintained. At the time when the rules were made, computers were not an option. The rules have not been modified since then, unfortunately, and still apply as they were.
Only Karnataka and AP have modified the rules to provide for automatic approval for electronic records. But you still need to inform the concerned authorities. In all other states, you need to take specific approvals.
Different Ways to Comply
1. Maintain the records in manual registers with manual writing.
2. Maintain records in electronic form with the approval of the department. Please note that approval for electronic records is approval to maintain in software that is tamper-proof and has a detailed audit trail. Therefore, records in Excel do not qualify or meet the requirements. It's a sure and direct non-compliance. Courts will not accept those records as they can be tampered with at any time by anyone. Some will tell you that Sec 4 of the Information Technology Act 2000 allows electronic records. That's a fallacy. Sec 4 specifies that you can maintain electronic copies of any record that is required by law to be maintained in hard copy. So, it means you can keep PDF/a copies of your records (PDF/a is a tamper-proof encrypted copy).
3. Take a print of all records every month, bind them as a set, and keep them as the hard copy records of the registers. That will be allowed by the authorities. It does not say in the act that it needs to be written in pen. However, wage registers, etc., which need to be signed must be signed in the original bound copies.
4. Where none of the above work, you have the option of taking prints of the records and pasting them in the register. That is followed by many companies. It has the advantage of being non-tamperable and still saves manpower by the use of electronic records.