The problem is that we don't know the changes that a springer fork will put into both the rake and trail of your current fork. I had a similar problem with the current bike I own now. I installed a suspension fork in a late 90s mountain bike frame. The problem I have was that the fork was too long and that cause the bottom bracket to be too high making the bike unstable. What I had to do was to substitute the suspension fork for a rigid fork that was slightly longer than the one that came with the frame. I have had no problems with stability in my current setup.
A good idea is to measure the length of the fork tubes and to see how far out from the fork crown the fork ends protrude. Hopefully if your Springer doesn't match it will be close enough to where your bike does not become unstable.
mike