There is this process that a leaving coworker wrote using (I feel) outdated software. The issue is anytime there is an error I have to consult with said coworker to get it fixed because no one else in my department knows work this software either. So I want to replace his process before he leaves. Should I let him know that I will replace his process and possibly offending him? or just replace it without telling him since he is leaving anyways.
There is nothing kind in telling that the first thing you'll do when he leaves, is throwing his work in the trash. Unless you have a personal need to make a point or be unkind, I would suggest you don't do it like that.
I would use the situation to get every piece of information out of this persons head and into the specification for the replacement system. "Outdated, I feel" is very vague - there is a vast difference between "This MS-DOS based software only runs on 32-bit Windows 10 machines, so updating now is due dilligence" and "I don't like this software because Outlook365 has something much nicer". It might turn out that the price for updating instead of just learning the existing software is much higher than you expect.
If you sell this right, this can be highly beneficial for both the employee, the company and yourself.
If you change the wording to 'updating' rather than 'replacing', you signal the process is necessary - and might have an easier time extracting valuable information from the soon-to-depart colleague. He probably knows that the process is very much tied to him so he will probably expect some hand-over at the very least.
A more constructive move could be involving him in creating 'Process v 2.0' with requirements like:
- Process must be performed by multiple people
- Update technological stack (if necessary)
- New business enhancements
If he had to create the process from scratch today, it's quite likely that he would make different choices. Find out what they are.
The most important point is to avoid stepping on his ego - and that can probably be accomplished by demonstrating that his process and opinions are valued.