Just opening mapy.cz (which just uses the Openstreetmap data in that area, but in a graphical way I really like) shows a very dense network if hiking trails in Luxembourg. Some go along roads, some not. Sometimes you have a choice between a pilgrimage route that mostly uses roads (like Jakobsweg that is going through Vianden) or hiking trails that go more across the hills. Depending on whether you want to follow one particular numbered trail or you wheter you do not mind to follow some more complicated plan, you have plenty of options. E.g., this kind of route mostly avoiding roads.
I have hiked in Luxembourg and the country is perfectly suitable for it. On the long distance trails as well as away from them.
Do realize that most of the trails will take longer than road routes and that many of the roads can get traffic heavy for their size.
I also never hiked near Luxembourg city, more in the north, Wiltz-Clervaux area and in the east, around Echternacht.
The country is not as public transport heavy as some of its neighbours but many places can be reached by bus or train if hiking takes longer than planned.
The GR5 crosses Luxembourg North to South, mostly along the Eastern border with Germany and the Mosel valley. Vianden is on this route, Luxembourg is not. From Echternach or Beaufort, you could however use some part of the Mullerthal trail routes to get quite close to Luxembourg. You could consider using some other form of transportation for the last 15-20 km between Bourlingster and the city.
Alternatively, walking all the way to Schengen along the Mosel valley would seem like a worthwhile goal in many ways. You could also stop in Wasserbillig to catch a train to Luxembourg. The distance would however be longer and maybe more suitable for a three-day or four-day trip.
There are apparently numerous long-distance hiking trails in Luxembourg, including the trans-european E2 and E3 trails (although neither of these go to Luxembourg city). However, there appears to be no trail that covers the specific route you seek to do. You could however complete your journey by combining several different waymarked routes, although as they are not entirely direct, it may take you longer than two days.
There is a map of waymarked long distance trails at https://hiking.waymarkedtrails.org/#?map=10!49.8017!6.1476
Although for your purposes there is a notable gap between Ettlebrook and Mersch that you would have to either go around, or fill in with hiking trails or roads that do not form part of a long distance route.
I have no personal experience of Luxembourg hiking, so cannot speak to how the signage or condition of these routes are, or what maps would be most useful for navigation.
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