Unfortunately, with KTP, it isn't simply dumping power into one end and watching it shit out a stream of photons through the other.
Several issues come into play here; power density is one of the most obvious. You might think that 2.5W seems like a lot of power, but frankly, it isn't. Second harmonic generation (frequency doubling) has an extremely non-linear efficiency curve- the higher the power, the higher the converstion efficiency becomes. If the power density is too low, you won't get anything out at all.
To put it into perspective, your dinky 5mW green pen laser has WATTS of intracavity power at any given point. Said power is concentrated as a spot that's micrometers wide.
Shooting a diode through a KTP doubler won't get the power density you need, and not only because it makes one pass through the cavity.
Remember that power density is a combination of area and power- in the pen laser, the 1064 beam is only micrometers wide. With a diode, the spot will be significantly bigger.
Now, assuming you got the diode down to a small enough point, you'll also have issues with phase-matching the diode to the KTP. Considering that most diodes at that power are horrible multi-mode, multi-emitter devices, it certainly won't be easy. And assuming you could phase-match it perfectly (which is damn near impossible), it'd be just as hard to get the power density needed.
Anyone remember the directly-doubled Novalux Proteras? They used a special VESCEL diode (which produced a clean, Gaussian beam with very little astigmatism), which also had an external cavity. The cavity didn't just cover the laser diode itself; the doubling optic, the LBO crystal, was also part of the cavity. Consequently, the power within the cavity was higher by magnitudes than not only what was being pumped in, but also what was being emitted. Those diodes are extremely sensitive, but it was the only way to achieve direct doubling.
So, assuming you had an external-cavity, single-emitter 2.5W 808nm diode, you have a slightly bigger problem.
KTP is a glitch. By some quirk, it's brutally efficient at doubling 1064nm. By the same quirk, it can't be phase-matched to double below approximately 500nm, and it won't double at all below 490nm (if I remember correctly).
Consequently, you're left with other options including LBO (which is annoying to work with for more reasons than one) and BBO. Neither of them have the efficiency of KTP.