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As Jonathan said below, you cannot avoid that menu, but doing the specific selection of faces may help you out.

There are two ways:
Selection by C:
Press C to make easier selection of faces you want to delete by clicking and moving mouse on the faces and delete Faces, you can change the size of the selection cursor by scrolling in and out middle mouse button.

Shift + Left-Click:
It can also be done by Shift and clicking the faces to make selection.

Delete all the selection with only one click and your are done.

As Jonathan said below, you cannot avoid that menu, but doing the specific selection of faces may help you out.

There are two ways:
Selection by C:
Press C to make easier selection of faces you want to delete by clicking and moving mouse on the faces and delete Faces, you can change the size of the selection cursor by scrolling in and out middle mouse button. You can also Deselect incorrect selection by pressing middle mouse.

Revise:
Press C and:
Left click and Drag to Select.
Middle Click and Drag to Deselect.

Delete all the selection with only one click and your are done.

As Jonathan said below, you cannot avoid that menu, but doing the specific selection of faces may help you out.

There are two ways:
Selection by C:
Press C to make easier selection of faces you want to delete by clicking and moving mouse on the faces and delete Faces, you can change the size of the selection cursor by scrolling in and out middle mouse button.

Shift + Left-Click:
It can also be done by Shift and clicking the faces to make selection and delete.

Delete all with only one click and your are done.

As Jonathan said below, you cannot avoid that menu, but doing the specific selection of faces may help you out.

There are two ways:
Selection by C:
Press C to make easier selection of faces you want to delete by clicking and moving mouse on the faces and delete Faces, you can change the size of the selection cursor by scrolling in and out middle mouse button.

Shift + Left-Click:
It can also be done by Shift and clicking the faces to make selection.

Delete all the selection with only one click and your are done.

As Jonathan said below, you cannot avoid that menu, but doing the specific selection of faces may help you out.

There are two ways:
Selection by C:
Press C to make easier selection of faces you want to delete by clicking and moving mouse on the faces and delete Faces, you can change the size of the selection cursor by scrolling in and out middle mouse button.

Shift + Left-Click:
It can also be done by Shift and clicking the faces to make selection and delete.

Delete all with only one click and your are done.

As Jonathan said below, you cannot avoid that menu, but doing the specific selection of faces may help you out.

There are two ways:
Selection by C:
Press C to make easier selection of faces you want to delete by clicking and moving mouse on the faces and delete Faces, you can change the size of the selection cursor by scrolling in and out middle mouse button.

Shift + Left-Click:
It can also be done by Shift and clicking the faces to make selection and delete.

Delete all with only one click and your are done.