string eng = "qwertyuiop[]asdfghjkl;'zxcvbnm,.QWERTYUIOP{}ASDFGHJKL:"ZXCVBNM<>`~ёЁ";
string ru =  "йцукенгшщзхъфывапролджэячсмитьбюЙЦУКЕНГШЩЗХЪФЫВАПРОЛДЖЭЯЧСМИТЬБЮеЕеЕ";
for (int i = 0; i < eng.Length; ++i)
  if (query.Contains(eng[i]))
    query = query.Replace(eng[i], ru[i]);

public sealed class Replacer
{
    private readonly Dictionary<Char, Char> _dictionary;

    public Replacer(String sourceSymbols, String targetSymbols)
    {
        if (sourceSymbols.Length != targetSymbols.Length)
            throw new NotSupportedException("sourceSymbols.Length != targetSymbols.Length");

        Int32 count = sourceSymbols.Length;

        Dictionary<Char, Char> dictionary = new Dictionary<Char, Char>(count);
        for (int i = 0; i < count; i++)
            dictionary.Add(sourceSymbols[i], targetSymbols[i]);

        _dictionary = dictionary;
    }

    public void FixCharacters(ref String query)
    {
        if (String.IsNullOrEmpty(query))
            return;

        unsafe
        {
            Int32 index = query.Length - 1;
            fixed (Char* chPtr = query)
            {
                while (index >= 0)
                {
                    Char oldChar = chPtr[index];

                    Char newChar;
                    if (_dictionary.TryGetValue(oldChar, out newChar))
                        chPtr[index] = newChar;

                    index--;
                }
            }
        }
    }
}

static void Main(string[] args)
{
    String eng = "qwertyuiop[]asdfghjkl;'zxcvbnm,.QWERTYUIOP{}ASDFGHJKL:"ZXCVBNM<>`~ёЁ";
    String rus = "йцукенгшщзхъфывапролджэячсмитьбюЙЦУКЕНГШЩЗХЪФЫВАПРОЛДЖЭЯЧСМИТЬБЮеЕеЕ";

    Replacer replacer = new Replacer(eng, rus);

    for (int i = 0; i < 10; i++)
    {
        String query = $"Hello World {i}";

        replacer.FixCharacters(ref query);

        Console.WriteLine(query); // "Руддщ Цщкдв"
    }
}

public static class LangConversion
{
    private static readonly Dictionary<char, char> engToRu = new Dictionary<char, char>();

    static LangConversion()
    {
        var eng = "qwertyuiop[]asdfghjkl;'zxcvbnm,.QWERTYUIOP{}ASDFGHJKL:"ZXCVBNM<>`~ёЁ";
        var ru = "йцукенгшщзхъфывапролджэячсмитьбюЙЦУКЕНГШЩЗХЪФЫВАПРОЛДЖЭЯЧСМИТЬБЮеЕеЕ";
        for (var i = 0; i < eng.Length; i++)
            engToRu[eng[i]] = ru[i];
    }

    public static string Fix(string str)
    {
        var sb = new StringBuilder();
        foreach (char c in str)
        {
            char fixedChar;
            sb.Append(engToRu.TryGetValue(c, out fixedChar) ? fixedChar : c);
        }
        return sb.ToString();
    }
}

Исходный вариант: 6480мс
Dictionary:       2330мс