What are you defining as 'very light'. Even the best of them are bricks when compared to conventional equivalents. What is light to a lumbering hulk like me might seem like an anvil to a feeble weakling like Dirk or Dave7
You then have the second problem of there being no standard measuring method for bicycle weights. Some quote without tyres, some without pedals, some ready to ride...and of those that do quote there is then no industry standard sizing schemeto compary weight for weight between manufacturers. When someone says a bike weights X kg, what exactly does that actually mean? The anseer can differ wildlymfrom brand to brand.
I'm sure its not an impossible ask, and your budget is very healthy. In your position id start scoping out some retailersmin person, because with that budget to spend it is they who should bendoing this dokey work for you.
I hope your quest goes well and you make a decent recovery.