Hi Bob. I am an Excel user like you.
You are on the right track, but you are skipping a step. In the window you show above when you right-click the sheet tab you need to change the first dropdown for "To Book:" to New Book. Then be sure to check the box for Create a copy or Excel will move the sheet out of your workbook.
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When you click OK with those settings changed Excel will open a new workbook named Book 1 or similar with only that sheet in it. From that new workbook you can email it, and since that is the only sheet in the new workbook that is the only sheet that will be emailed. You do not need to save the new workbook. Just email it and then close it without saving.
One additional hint: If you have formulas in the sheet you are emailing, you can copy all of the data on the sheet and paste values to remove all of the formulas before emailing. Since it has been copied from the original workbook this will not affect your original sheet.
To email it, in the new workbook click on File>Share>Email>Send as an Attachment or one of the other options if desired which will open an email window where you can enter your addresses and send.