Why remove the sleeves at all? Unless you really want an Inverness cloak, most people would have no idea what one is anyway. Sleeves are warm! Sleeves under a cape are warmer! I've worn a full-length lined wool cloak with armholes and a cape, and while you can easily keep your arms warm by folding them under the cape, if you need to use your arms then they get a little chilly since you're lifting the cape up. I think the sleeves look fine on your greatcoat.

Andrew.