Answer:
The Fuqaha have given permission to make Tayammum when a person fears that he will miss the whole Janazah Salaah. Seeing that your situation is similar, Tayammum will be permissible for you. Therefore you can suffice on making Tayammum and participate in the Janazah Salaah without having to first take a bath or make wudhu. Tayammum is permissible for both hadath e asgar (when in need of Wudhu) as well as hadath e akbar (when in need of a bath). However, after completing the Janazah Salaat an earnest effort must be made to make arrangements for a bath. It is highly undesirable for one to stay in a state of najaasat (impurity) especially when it is possible for one to have a bath. (Fatawa Hindiyah vol 1 pg 31)
