He is unable to do the weight on Burton Port for his retained yard of Nicky Henderson, so is set to partner the Irish raider for Mouse Morris.
Geraghty was in the plate when the seven-year-old finished third behind Kauto Star and Sizing Europe at Down Royal earlier this month.
“I can’t ride at 10st so it looks like I’ll be riding China Rock,” said Geraghty.
“He carries 10st 4lb, and that’s the lowest I can do anyway. He ran a good race the last day so I’d be hopeful he'd run well on Saturday.”
Andrew Tinkler will now take the ride on Burton Port.
The six-year-old has won five of his six starts over fences, with his only defeat coming at the hands of Weapon’s Amnesty in the RSA Chase at the Cheltenham Festival.
Tinkler said: “It’s a brilliant ride to get. I rode a winner on him last year and Denman being in the race has given me a big chance.
“I can do 10st easy. I’m about that now and it will just be a matter of losing a couple of pounds during the week.”
Ian Williams expressed delight after Weird Al enjoyed a schooling session under big-race jockey Paddy Brennan yesterday morning.
“Paddy Brennan came in to school him and he jumped six fences with Othermix and Wayward Prince,” said Williams.
“We were both delighted with him and Paddy was thrilled, so he’s firmly on course for Saturday’s Hennessy.
“We’ve been quite fortunate that we’ve got all to get done out of the way and while the weather doesn’t look promising, as long as they get the meeting on it won’t be against us.
“He ticks a lot of boxes and we can’t do any more, so we’ll see how we get on.”
Ferdy Murphy believes the fact Graham Lee can ride at 10st is a big positive for the chances of the Harry Findlay-owned Big Fella Thanks.
“We’re happy with him and all his preparation has gone well,” said Murphy.
“He was a bit unlucky at Carlisle as he got to the front too soon, but that won’t happen again, I shouldn’t think, as Graham will drop in and bring him late.
“Graham can do 10st no problem, which is a big plus for us and the drier the week we have, the better for him.”