The ornamental design of a body for a compactdesk top fan, as shown and described.
FIG. 1 is a right side front perspective view of a body for a compact desk top fan showing my new design;
FIG. 2 is a rear perspective view thereof;
FIG. 3 is a front elevation view thereof;
FIG. 4 is a right side elevation view thereof;
FIG. 5 is a left side elevation view thereof;
FIG. 6 is a rear elevation view thereof; and,
FIG. 7 is a top plan view thereof.
The broken line showing of a grill, button and a stand is included for the purpose of illustrating environmental structure and forms no part of the claimed design.