Legato/tapping String Noise

Hi. This is my first post here on GMC, been a member for a few weeks now. I have been trying to play this lick which goes something like:

T T

20--19--15-------------15--19--20--19--15------------------
-------------17------17-------------------------17------17----
-----------------16-----------------------------------16--------
-----------------------------------------------------------------
-----------------------------------------------------------------
-----------------------------------------------------------------

T T T

15--19--22--19--15--19--22--19--15--19--20--19--15-----------------
--------------------------------------------------------------17------17----
-------------------------------------------------------------------16-------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------

The idea is that you tap the 20's/22's and then the rest is pure legato. My problem comes when you switch strings, i always seem to get string noise when i speed it up. When You try and do this sort of fast string switching legato is it best to have your left hand fingers vertically so they touch only the string you are playing or slightly angled so they hit (but not fret) the string below? In pavels lesson on legato i seem to recall him saying u need your fingers to be vertical and then just use the index finger to mute the strings but if you are playing these sort of sweeping patterns your index finger has to do hammerons as well so it can't always mute the strings. The only way to mute the strings below the ones you are playing seems to be to fret the strings with your fingers at an angle but then sometimes that seems to get string noise anyway when you start playing faster. Even when you don't fret the notes just coming near the strings seems to generate noise. Any help would be appreciated....Would anyone judge me if i went for the easy solution and got one of those noise gate things or whatever they are..... lol