Midfielder Vancooten was forced off during the second half of the 3-0 defeat at Lincoln on Boxing Day with what is suspected to be a fractured cheekbone and did not make the bench for the defeat to Crawley.
Beautyman has been having treatment on a thigh injury and he also missed out against the Red Devils.
Ben Kennedy, Alex Samuel and Matt Gooden all started on Saturday having initially been doubts, with Samuel brought off after 75 minutes.
Gary Johnson could select from the same squad that drew with Newport for the trip to Broadhall Way.
Brian Graham started after coming off the bench against Yeovil following a hamstring injury but came off in the 66th minute to be replaced by Danny Wright, who is pushing for a start.
Freddie Hinds – another man looking to get into the starting XI recently – was an unused substitute against Boro.
Defender Jordan Cranston (hamstring), forward Jaanai Gordon (knee) and defender Jordon Forster (Achilles) remain long-term absentees.
Burton midfielder Martin Samuelsen will use the international break to recover from illness after pulling out of Norway U21's games.
Jonas Lossl is staying 'optimistic' over Huddersfield's chances of survival this season and has urged his team-mates to 'go for it'.