Well, TWebbrowser (in D11) has a protected method
function GetEdgeInterface: TEdgeBrowser;
To get at it you can use a cracker class, e.g. declared in the implementation section of the form unit containing the TWebbrowser control.
type
TWebBrowserCracker = class(TWebbrowser);
In your code you can then do something like
var Edge: TEdgeBrowser := TWebbrowserCracker(Webbrowser1).GetEdgeInterface;
if Assigned(Edge) then begin
Edge.UserDataFolder := SomeDirectory;
Edge.ReinitializeWebView;
end;
Completely untested, so use at your own risk!