OK, I was reluctant to directly answer the question, "How will the handling be affected by a new fork", earlier because I had forgotten some of the details but now I've done some reading and reminded myself so here goes.

Short answer. If you fit a new fork with less Rake (Offset) to this frame you will slow down the steering and it will feel sluggish. All that Rake is there to speed up the steering by compensating for the VERY relaxed (68 degree) head tube angle.

Longer answer. The concept/measurement that is important here is, TRAIL. See the link I posted above for a diagram and it works like this. Draw a line along the axis of the head tube to the ground. Draw another line from the front axle vertically to the ground. The point where the vertical line from axle hits the ground is ALWAYS behind (trailing) the point where the line parallel with the head tube hits the ground. The less this distance, the more direct and fast the steering feels. The greater this distance the slower and more stable the steering feels.

Now, lets say you have one fork with a fixed rake already made and you fit it to bikes with different head tube angles. The bike with the steeper head tube angle (larger number, lets say 72 degrees) will have LESS trail(shorter distance between where the two lines fall on the ground), and more direct feel to the steering. The bike with a slacker head tube angle (lets say 68-69 degrees) will have more trail (greater distance between where the two lines fall on the ground) and less direct steering but feel more stable.

Now, the head tube angle is not the only factor in this equation that can be adjusted. You can change the rake of the fork. So, lets say we have a frame with a 68 degree head tube angle. To speed up the steering and make it feel more like a bike with a steeper head tube angle what you do is fit a fork with a greater Rake (offset). This pushes the axle forwards so its closer to the line from the head tube and consequently reducing the Trail.

With me?

It can get more complicated than this and wheel size is another factor in calculating Trail.