I don't have a Draconic Aegis to try on, but I have a couple other shields that seem to work fine with this armor.
Can't provide screenshots right now, but among the skins I know about, neither the Tormented Shield nor the Darkwing Defender show clipping issues with the Silver Eagle.
The former is vertical and slightly detached from the left arm, so it's never in contact with the left glove, hence it never clips.
The latter is pretty thick, concave and tilted, so the left hand is wrapped around under the shield surface and no evident clipping occurs.