This is a difficult one to judge. We don't know what particular compromise in the switch design has led the makers to specify it at 2000 watts
It certainly won't be the absolute power being switched.
In some cases it might be the continuous current being drawn and in which case very few domestic routers are going to be worked at full load for long periods enough to heat up the switch contacts - so probably ok
If however the limit is due to the contact materials and the effect of the high voltage spark when turning on and off (particularly the latter) then the contacts will gradually be eroded away, leading to high resistance and the heat generated for a given load will increase leading to early failure. so not a good idea to use it
There will be design and manufacturing tolerances and the rating will be based on the worst case - so the switch is quite likely to be fine.
What would I do? Possibly buy two, keep one as a spare and keep an eye on the switch to see if it gets warm after long heavy routing sessions. If all is well - then fine. If it does fail then it is an easy swap with no need to change the mountings etc.
To be really sure then always use an adequately rated switch, or do as I would and get used to how it behaves and note if behavior changes and investigate before anything dramatic happens in the middle of a time critical job.
If you are making your living using this router, then don't compromise. Machine downtime will cost you much more than the savings on an inferior switch.
HTH
Bob