Budd Fox was entered for Tuesday's Brierly Steeplechase (3450m) but was not among final acceptors on Friday, however he is also entered for the Novice Steeplechase (3450m) on Wednesday and the Grand Annual Steeplechase (5500m) on Thursday.
Dwyer has set Budd Fox for the Annual but is reluctant to run in the marathon if the track was too wet.
He said Budd Fox was not sharp enough to tackle the classier jumpers in the Brierly over the 3450m but added it would be a different story if he elected to start in the Novice on the second day.
"He's more of a grinder, but in the novice, he might be the best horse and get away with it," Dwyer said.
"I've had him set for the Annual, but it's a bit tricky because he doesn't like wet tracks, so it might be a bridge too far if it is wet, especially over the 5500 metres.
"We don't need to bottom him out.
"He's a nice horse and we'd like to go to the Jericho Cup again at the end of the year, like we did last year, and he's got a couple of big years ahead of him with the steeplechasing."
Budd Fox is an inexperienced jumper switching to steeplechasing after only two hurdle starts.
Dwyer said steeplechasing, with the slower tempo and bigger jumps suited the gelding.
Budd Fox made his steeplechasing debut with a narrow second to Valac at Pakenham on April 18 and with established stars Gold Medals and Zed Em falling by the wayside, Dwyer felt the Grand Annual could be the right race for the up-and-coming jumper.
"He trialled super before his first steeplechase start and he made a little mistake down the back and almost got there, so a longer trip will help him," Dwyer said.
"It's not a vintage year for steeplechasers and he's a good, safe jumper and will appreciate the extra trip, so why not have a crack at it."