Would I be taking a big risk?

Here is the deal. I started doing my own web sites for my business maybe 15 years ago +/-. I started using Front Page and then 4 or 5 years ago started to use DreamWeaver. I have 8 or so web sites for my business two of which are the ones I would consider the main ones. Of those two the one that is most important was set up long ago when I was still using FrontPage. I bought a theme when I set it up and as far as design and colors it looks decent. I have tons of good content. We generate enough business from it that we can't keep up and I get compliments on it (maybe not as many as I used to but still compliments and really no complaints. With the Google change in giving priority to mobile friendly or responsive sites I decided that later on this year I would update the site using Wordpress.

I am going to do a couple of my less important sites with wordpress first just as a learning experience. Actually I started on one which is currently a mess but it is one that really had little purpose anymore and little traffic so I don't really care.

Now here is my concern. I had not checked to see how we do on a search for quite some time. Currently on the two most important search terms, one being the type of equipment we make and the other the process you do with that equipment we come out # 2 on one of the terms and # 3 on the other. (not counting the 3 or so paid results)

There is a saying "If it ain't broke, don't fix it". If I redo the site, I could easily end up on page 17 of the search results. Should I take the gamble or play it safe and not fix it?