As soon as you define "webbased look and feel" we'll have your answer. :)
Seriously, there has been some discussion c.l.p.tk of "skinning" Tk apps, so that they have an internally consistent graphic theme which differs from the rest of your applications. We also have
Petruchio's
Tk::Style module, which allows for something similar as I understand it. But if your clients want a web browser experience, what's wrong with ripping the Tk interface from your application and replacing it with a CGI interface? Of course, I make this sound trivial, and in some ways for a well-designed application it would be trivial. But it's not, since direct GUI interaction is not the same as turn-based HTTP interaction.
Some tricks you can try might include embedding widgets into your Tk::Text object (and if you don't have one, looks like you'll get to figure one out), and building a toolbar with some fancy icons and some standard browser notions on it. By putting your widgets into the Tk::Text object they will be drawn a lot more like the elements on a web page.
But me personally, I'd ask the client what exactly their problem with the current interface is. By removing borders from buttons, and setting backgrounds to a consistent color, and stuff like that, you can make your app look a lot less like a bunch of glued together GUI-construction-kit pieces and more like a solid whole. Again,
Tk::Style looks like it would be helpful in this endeavor.