I don't think they've come up with "good enough" consumer-retail handwriting-to-text software, yet.
For greatest safety, though, I would scan the journals: Paper is so easily destroyed. I'd scan to the best resolution possible, and perhaps someday there will be a way to convert those images to text. Save the paper journals, if you've got room, but more importantly, make sure you have the data files of the writings in at least two locations, each location not likely to be affected by a disaster at the other. Also, if you're going to store this data on CD-Rs or DVR-Rs, make sure you plan on copying them every five years or so, just in case. (Discs you burn yourself don't really last forever.) If you're storing the data on hard drives, you should also figure that you're going to have to move the date at least every five years to ensure its integrity. (The only mostly-maintenance-free means of storing electronic data is magnetic tape. Either that, or store one copy with an online storage provider, such as Dell DataSafe, or the free Yahoo Briefcase Yahoo Briefcase. While those companies don't guarantee data integrity forever, the reality is that they do all the right things to ensure your stored data doesn't degrade -- but of course, only if you're continue to use their service regularly.)