Nanai was whacked with a grade three dangerous contact charge on Friday and will miss four games if he takes the early guilty plea, ruling him out of Origin I in Adelaide on May 31.
In the unlikely event he succeeds in having the charge reduced, Nanai could shave time off his ban.
But the back-rower will have his ban increased to five games if he unsuccessfully fights it.
Cowboys coach Todd Payten defended his forward after the 44-6 loss to the Sharks.
"I didn't think he made a great deal of contact on the back of (Hamlin-Uele's) leg," Payten said.
"His arse and hips were away from the back of his leg.
"Braden jumped up pretty quickly to throw the ball at him, so it mustn't have been too bad initially."
The Sharks suspect Hamlin-Uele has suffered a medial collateral ligament injury and have sent the prop for scans.
Nanai was not alone in being charged, with Payten relieved prop Coen Hess (tripping) and fullback Scott Drinkwater (leading with the elbow) can both play next week after accepting fines.
The trip to Cronulla proved to be a costly night for the Cowboys, who are off to an underwhelming 3-6 start in 2023 after reaching last year's preliminary final.
Chad Townsend limped off at Shark Park with a calf injury, while promising fullback Tom Chester suffered an anterior cruciate ligament tear.
It remains to be seen whether Townsend will join Jason Taumalolo, Griffin Neame and James Tamou on the sidelines when they face the Sydney Roosters in the NRL's Magic Round next weekend.
