Will a sharpener for a wider edge ruin a knife with a narrow edge?

If you sharpen it with a 20 degree edge, it will remove material until it matches the 20 degree bevel.

It is up to you whether you like this better or not; however, if you selected this particular knife because you like the way it feels and cuts, the 15 degree bevel may be a contributor to that.

Will it harm the knife? No, but it will change its performance characteristics.

Sharpening Supplies provides a table of common bevel angles for various purposes, but indicates it is mostly up to personal preference. They indicate 20 degrees is common for chef's knives, and go on to say:

The lower the angle the sharper it becomes, but it also becomes less durable and more prone to chipping. If you seek a very durable edge, a larger angle is preferred because it can withstand more than the thinner edge of a low bevel angle.

The angle of the edge should adjust itself when sharpening anyway.

Most professional chefs will probably use a sharpening steel or stone and will just sharpen their knives in a way that feels natural.

It helps to understand the way a knife edge becomes dull. If you were to zoom in on a knife edge you would see what look like hundreds and thousands of teeth, much the same as on a saw blade. When the knife is used these teeth become misaligned, and because they are so tiny knife blades require regular sharpening.

A 15 degree blade kept at this level will consequently feel sharper but for a shorter period of time and will require more regular sharpening. Conversely a 20 degree blade will hold an edge for longer and will cut as if "sharp" for longer but will not give you quite the same smooth easy feeling. It is similar to thinking about the difference between a razor blade and a non-serrated steak knife. I very much doubt many people will sharpen, or change their steak knives much, but they will (or should) change their razor blade frequently.

Chefs who use a steel or sharpening stone will give their knives an edge which is unique to them due to the unique angle of sharpening on either side of the blade and the direction the knife is sharpened (some sharpen away from the handle and some sharpen towards it). Which is why you should never let anyone but you sharpen your knives.

In short, as long as you are consistent the blade should be fine and last you a very long time. Victorinox knives are nice. I had a couple of them when I was working in kitchens and they should last you a very long time if looked after. My head chef's filleting knife had a blade that was as wide as a fat pen he had it that long and sharpened it that much!