Example how ArcGISHttpClientHandler.HttpRequestBegin event can be used to rewrite WMS requests.

ReplaceCrs84WithEpsg4326.cs

private static void ReplaceCrs84WithEpsg4326(object sender, HttpRequestMessage e)
{
    string rawQuery = e.RequestUri.Query;

    // Skip requests without a query
    if (string.IsNullOrEmpty(rawQuery))
        return;

    // For convenience, parse query as a Dictionary
    var queryParameters = System.Web.HttpUtility.ParseQueryString(rawQuery);
    var queryDict = queryParameters.AllKeys.ToDictionary(
        k => k.ToUpperInvariant(),
        k => queryParameters[k].ToUpperInvariant());

    // Skip requests that are not WMS
    string serviceParam;
    if (!queryDict.TryGetValue("SERVICE", out serviceParam) || serviceParam!= "WMS")
        return;

    // Skip requests that don't use CRS:84
    string crsParam;
    if (!queryDict.TryGetValue("CRS", out crsParam) || crsParam != "CRS:84")
        return;

    // TODO: if necessary, apply additional checks here to limit which WMS services are affected

    // Replace "CRS:84" with "EPSG:4326"
    queryParameters["CRS"] = "EPSG:4326";

    // Swap lat/lon in the requested coordinates
    var bbox = queryDict["BBOX"].Split(',');
    var swappedBbox = bbox[1] + ',' + bbox[0] + ',' + bbox[3] + ',' + bbox[2];
    queryParameters["BBOX"] = swappedBbox;

    // Replace the original query with our modified one
    var uriWithoutParams = e.RequestUri.AbsoluteUri.Split('?').First();
    e.RequestUri = new Uri(uriWithoutParams + '?' + queryParameters);
}