With the right Unicode characters, the old character encodings shouldn't make much odds. The tricky bit may be converting existing ASCII art into Unicode - at which point you need to know the original encoding.
The relevant code charts will be listed on the Unicode "symbols" charts page. In particular, I suspect you'll find the box drawing and block elements charts useful.
You'll need to make sure that your page uses a font which contains the right characters, of course...
As an example, you can render this:
┌┐
└┘
With:
<pre>┌┐
└┘</pre>
Not quite a proper box, but getting there...