Yes, a script can do this.
Save as | Excel or Export Records can generate the the needed Excel file.
Send Mail can send an email to your recipient with the Excel file specified as an attachment.
This can be done in a loop where the loop steps through each client record, generates a find, creates/exports the file, sends the mail then repeats with the next client record.
Do you know how to create scripts?
Are you familiar with these script steps?
I will try that. I've done simple scripting so this will be a good exercise tom improve even more.