Membership Contribution Page for Cash or Check Payment
I presume you are trying both to simplify things for your Finance Administrators and restrict who has direct access to CiviCRM, but I don't think using a front-facing CiviCRM contribution page will accomplish those aims. 

If monetary contributions are involved then a front-facing CiviCRM contribution page will need either to have a payment processor specified or to have the "Pay later option" ticked. Once the pay later option is enabled then the email field will be pre-filled when an existing contact is selected.  

However, if the pay later option is ticked then the payment is recorded as "pending (pay later)" so the Finance Aministrators will still need direct access to CiviCRM to record the payment.  You also then have a two-step process rather than a one-step process.

It might be easier to use permissions to restrict what Finance Administrators can do in CiviCRM and train them to use a rear-facing form.

And just for completeness for other people looking at this Q&amp;A, at this time CiviCRM pricesets cannot be used with webforms.