Can I change the shift solenoid in my century without removing the transmission on 1993 Buick Century

My 93 Buick century . Will go in reverse .. first and park will not shift out of 1st....fluid is used but don't look to bad no metal shavings or nothing... what's my problem car acts like the c....converter is clogged too runs and idols like crap... I've been all over the motor fixing vacuum lines little..... better but still chugs hard at idol and sometimes dies..... don't have much history on the car...I just bought it.... and if any one has a trans locally for less that 200 hit me back.

Asked by for the 1993 Buick Century
I would have it scan tested before you do anything with the trans