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If, however, you made the circle the same color as the blips...
That has the drawback of IFF decoders not being compatible though.
So there's no good way.
It might work if the IFF was 'built into' every playable ship via an included outfit. After all, in terms of plot, if you can build interstellar warp drives and massive spacefaring battleships, surely a simple IFF decoding chip should come as standard equipment. Of course, you can spin plot a milion different ways. You can, however, use something like what I mentioned as justification and make it work nicely, if you so desired.
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Does the graphic overlap the screen? My assumption is that the screen is lust laid on top of everything, and since it's part of the engine, you can't change its shape.
IIRC, the boundaries for most of the displays and status bars in the interface are defined in terms of their corner locations (?), so they have to be rectangular in shape.