If you want to make only few users as skill mandatory and few users as normal assignees i think its not possible with single assignment eligibility .
First try to separate skilled users and no skilled users in to two groups and add those respective persons into two groups
try this it might work
1) open your queue and go to assignment eligibility tab and open the record
2) then after opening you can see the assignment rule tagged to it .Open the assignment rule
and also tag the group which has skilled users as group members
3) There you can see enforce mandatory skills which should be checked in you case for skills users
Solution :
1)Create one more assignment eligibility record for the same queue
2) Create another assignment rule with enforce mandatory skills as unchecked and enable skills unchecked
3) Tag the assignment rule
4 )Tag the group which has non skilled users and save the record
Now try making agents available and see if it makes any difference in auto assignment
PLEASE MARK MY ANSWER CORRECT IF IT HELPS YOU
