Greg, first off, nice photo of the goose! A "fading Birder" myself, I just had to look that beautiful bird up ... here's what I found: http://www.birdsofbritain.co.uk/bird-gu ... -goose.htm
The Grafts: Let Them Alone
. I've got a tree-full of cleft and 'splice' grafts (about 7 individual limbs) on a 'Peach Plum' I'm trying to develop pollination limbs (of 'Petite,' & 'Green Gauge'). I look them over about twice a week, watching for 'nibbling.' If I find their leaves (always lagging slightly behind the base tree, thus more tender) are being nibbled, I'll smear some Tanglefoot
around the base of the scion, or the stubbed off limb -- having looked for and smashed the offending earwig / aphid / caterpillar...
I'm sitting here smiling . .
.. remembering myself all those years ago --- trying to think of anything and everything I could 'do' to speed the process, including 'breathing on them' -- assuming carbon dioxide was a 'growth enhancer.' Here are a couple of my concerns: that nibbling; a bird landing on them and breaking off the 'shoots;' children 'discovering' them; last and least -- hot weather, or 'sun damage.' For the most part, I've just taken my chances. It's very rare a bird will land and damage them; now that yours are so short, they'll probably not be viewed as landing twigs -- which has been the only problem I've had with birds. As far as heat, or sun, they should be able to take it, and thrive!
Don't even think about which one you'll 'remove.' You want them to grow as big, long and strong as possible this season.
Tip prune the shoots and tie them at a branch angle
with string this Winter
; and let them race to health again next season. Eventually, one will become dominant, but that doesn't mean the other will (as the British say) become redundant.
You want them to heal over that stub ASAP --- but there's little you can do to speed the process... And in this case, that may be your most difficult task! I can relate --- so follow that Goose!