After spending quite some time investigating this I discovered that you could not simply alter the stop word list (STOP_WORDS_SET) used by the StandardAnalyzer because when you inspect it, instead of returning a Hashtable it returns what is essentially a read-only representation of the Hashtable called an unmodifiableSet.

It turns out that not a lot of code is required to overcome this so I created a new analyzer that inherits from StandardAnalyzer and injected a modified stop word list into the base constructor. In case it is of use to anyone else here is what I've done.

using System.Collections;
using System.Linq;
using Lucene.Net.Analysis;
using Lucene.Net.Analysis.Standard;

namespace My.Namespace
{
    public class MyStandardAnalyser : StandardAnalyzer
    {
        public MyStandardAnalyser() : base(Lucene.Net.Util.Version.LUCENE_29, MyStandardAnalyser.ENGLISH_STOP_WORDS_SET)
        {

        }

        private static Hashtable ENGLISH_STOP_WORDS_SET  {
            get
            {
                var stopWords = Lucene.Net.Analysis.Standard.StandardAnalyzer.STOP_WORDS;
                var set = stopWords.Where(w => w.ToLower() != "will").ToArray();
                var charSet = new CharArraySet(set, true);
                return CharArraySet.UnmodifiableSet(charSet);
            }
        }
    }
}

I then amended the ExamineSettings.config file so that the ExternalIndexer & ExternalSearcher uses the new Analyzer.