Great question! I just happen to have the Prelude on my desk at the moment - you've got a really interesting project on your hands there, but quite a lot of work - good luck!
Hopefully I can add to jjmusicnotes really useful advice with some ideas that will make this a far simpler project for you.
Firstly, from your question, it seems like you are "half-way" to understanding the basic approach your project will need. You acknowledge, for instance, that "Cornets should represent most of the high passages…" Yes, this is likely to be the role taken by cornets in your arrangement and is a good approach. But, you also say, "Some parts are the same, and some correspond to obvious parts." This is not a useful approach; you would not simply copy trombone music from the Wagner into the trombone parts of your arrangement. Also, the question itself asks how to "approximate instruments" when arranging. This, again, is not always a useful approach; although a brass band is a beautiful ensemble, capable of a wide range of interesting timbres and techniques, it is never going to match the range of a full orchestra of winds, strings, brass and percussion. So, you should not simply be thinking about what will most sound like a cor anglais, for instance. Rather than trying to make your brass band version sound as similar as possible to the orchestral version (which will be very difficult), you should aim to use a range of contrasting instrumental colours available within the brass band instrumentation, just as Wagner uses a range of instrumental colours within the orchestra.
So what is the right approach?
Well, to understand how to go about your project, let me give you an example of a much simpler method of arranging; this will give you an insight into the different method your project requires.
If you wanted to arrange an SATB choral piece for string quartet, you have a very simple project. You could simply give the Soprano line to Violin I, Alto line to Violin II, Tenor line to the Viola and Bass line to the 'Cello. Okay, you have to remove the lyrics, check the ranges work okay and maybe change some phrasing, but essentially this is a one-to-one mapping of parts. It is like translating a single word from one language to another.
You cannot take this one-to-one mapping approach when arranging your brass band version of the Wagner. This is more like trying to translate a whole book; you need to understand the fundamental meaning of the text (or music in your case!) before creating the new version. Rather than simply giving music from one instrument of the orchestral music to one instrument of the brass band, you need to assess: what role this instrument plays in the original, what role groups of instruments play in the original and crucially what role different musical material has in the original (for instance, is it melodic, harmonic, part of the bass line, part of a countermelody etc.) You then assign this music from the original to instruments that are suitable for such a role in the brass band.
To complete this project successfully, you are not really arranging, you are re-orchestrating.
And yes, this is quite a lot of work. But there are two ways you can do this; one is a lot easier than the other.
Re-orchestrating the hard way.
Assess the role of all musical material in the original score. Assess which instruments (or groups of instruments) will effectively be able to perform each piece of musical material in your brass band version. This may change through your arrangement; musical material associated with particular instruments in the original may not always be associated with one instrument or group of instruments in your version. Instead, at any one time, you need to be thinking about which instrument or group of instruments are best able to play musical material within the overall musical texture.
A somewhat simpler approach.
Use a piano reduction of the original orchestral score (or four-hands piano, or piano and voice etc.) Well, this is essentially the same approach as above, but now the initial process of condensing the musical material of the orchestral score has already been done for you, meaning you can get on with the process of orchestrating straight away.
In reality, you will need to take an approach somewhere between the two. I would work from a piano reduction, but constantly refer to the orchestral score, to check that I am reflecting changes of timbre and techniques in the original orchestral version in the new version. But again, this needs to be approached with common sense; you are attempting to preserve interesting changes of timbre, texture, technique, tone and tessitura in the original when writing your brass band version. But you are not simply mimicking or copying the original. You can't give pizzicato instructions to your brass players, but how would you create a similar contrast of tone in your ensemble? No instrument in your ensemble may be able to easily play the flute part at the same pitch, it is more important that different pieces of musical material appear in the correct register relative to other music in your arrangement.
I could go on, but as jjmusicnotes pointed out, orchestration and arranging are an art; there are plenty of rules and useful approaches that can be learnt, but effective orchestration requires study, thought and practice.