We have written a document management system and would like to digitally sign documents using the web client. Our Java client application is already able to apply and check
Now you can do that. Web application based on PKCS#11 smart cards or tokens can be implemented by using the Silverlight version of NCryptoki. See http://www.ncryptoki.com
You have two chanches:
1) using the Silverlight version of NCryptoki and develop your own Silverlight User Control that implements your logic, a Digital Signature in your case, using PKCS#11 functions supplied by the smart card
2) using the JQuery plugin based on the above Silverlight version and implement your application in JavaScript by calling the PKCS#11 functions in JavaScript
Also, you can use the Silverlight version of NDigitSign (see again http://www.ncryptoki.com) that does all you need and can be implemented in any web browser.