From the thread title I as expecting this to be about your chances of a Wembley win
Most club's mascots are available for visits to birthday parties , weddings etc . It is very rare for them to be unable to sort your request for them to attend as clubs/ businesses that have a mascot type figure rarely only have only one . You don't always get the matchday mascot , but if not , you will get an identical look-a-like . It just won't have the moves that the regular mascot has .
The above post regarding the HFC experience seems good value for money , but I don't think it includes an actual party . Would be worth calling them and seeing if the have a room you could hire for a party after the tour .
Good luck , and happy birthday to her .