Can I batch data enter contributions using contact id instead of name?
Without coding? hmmm. 

CSV importing might work.
Contributions -> Import Contributions

The CSV can work with the internal ID

You would not have a nice screen with the batch import but only work with Spreadsheet/CSV's and import those.

But.. person responsible for either importing the CSV or doing the batch entry should be able to check if it makes sense what he did. Otherwise you could end up with very strange data due to a small mistake. So my advise is for you to also check your permission policy. Maybe someone else entering the info or give that permission to the church secretary anyway.