You’ve fixed it with tape. Neat.
You could have cut the current 3-pin plug off the cable and put a regular plug on but leave the earth disconnected. And with the wire stump suitably insulated within the plug body to avoid shorting.
as folks have described, most of these machines come with 2-pin plugs in EU and USA. And most folks suffer no problems using those awful 3-pin to 2-pin adapters when travelling many of which have a similar effect of not earthing a 3-pin plug.
corporate IT used to provide me with laptop, 2 ‘U.K.’ power adapters, 1 for my desk in an office, and 1 for travel. With 3 cables for the second adapter: 3-pin U.K., 2-pin EU, 2-pin USA. No death ensued.