"I got a lot of partially gutted TVs at an auction (All the same brand) and I'm trying to build a 'Frankenstein TV'.
I have a 13" unit with a working power supply board and tuner board in one set. I have another set with a 25" picture tube in it. I'd like to drive the big tube with the guts from the small TV. Does anyone know If I'll blow up my workbench if I attempt this sort of transplant?"
It won't blow up your workbench but the differences are probably significant enough that the performance would be unsatisfactory if it worked at all.
In addition, this may blow up the power supply board - kill the horizontal output transistor and/or low voltage power supply itself - as the required power levels are higher. If you have nothing to lose, power your Frankenstein initially through a series 100 W light bulb and Variac. Then you will be able to tell if you are even close with less risk of blowing expensive parts.
Of course, this does assume that all the organs your are merging are actually good to start with. Why do you you think they unloaded those TV carcasses?
While the same chassis may be used for 19" and 25" sets, going from 13" to 25" is likely to have many differences.