I once asked the salon guys exactly this after a purchase from their New Bond Street store and, unsurprisingly, they don't and won't offer an inflated replacement valuation.
RRP on this watch is just under 42.3k; Chrono is suggesting they're worth 64k (typically 20%+ over reality) and auction is seeing them sold in unworn condition - ie yours - at just under 50k.
The difference in retail cost versus replacement cost at auction is therefore relatively marginal so I wouldn't bother. It's not like the madness of Spring 2022 when Pateks and Rolex were trading at crazy money. Those days are long gone, IMO.
Nice watch BTW. I have the chrono version.