I happen to own a book which includes an brief interview with General William Burns, who was Brigade Commander of the 42nd Field Artillery Brigade at the time of the attack (Secrets of the Cold war by Leland C. McCaslin)
The interview focused solely on the incident. He did not go very deep into details and most of the interview is fluff.
Here's the wheat from the chaff
A bomb was set on a fuel storage tank in an attempt to cause either a diversion or a damaging conflagration, the tank was almost empty so the ensuing fire was minor.
There was a brief exchange of small arms fire but no penetration of the depot perimeter (apart from planting the bomb)
The guard detail responded as planned and reinforcements arrived from the 3rd Armored Division well within time limits for response.
No mention is made in the interview of US or RAF wounded or dead
General Burns also claimed in the interview that when several who participated in the attack were later captured they made an unusual claim. The claim was that there apart from the bombing there was no RAF involvement and that any small arms fire was the US shooting at deserters.
This stands in contrast to the wikipedia entry which mentions RAF dead and a repulsed attack on the armory.
It appears to me that the special weapons would have been kept at NATO site 4 in Giessen, which based on the maps and pictures found at this link
http://www.pbase.com/202mpco/west_germany&page=1
does not have any fuel tanks present (naturally you would want to keep your fuel tanks away from a restricted area since you would have to routinely access the fuel tanks and you don't want to risk a fire turning into a nuclear disaster) this leads me to believe that the RAF attacked Giessen Depot(a fairly sizable US base) but probably not NATO site 4
I think the most damage the RAF could do without active Soviet or East German assistance would be to lightly damage the bunkers at site 4 and kill some US personnel.
To gain access to site 4 for a brief period would require a much larger RAF, Spetznaz providing back up or massive US incompetence to a level that is at or near ASB.
For example soft buildings instead of bunkers, few guards/guards are all drunk/high/Gomer Pyle level incompetent, no ammunition provided to guards (last one not necessarily ASB)
So you gain access (Not a quick thing, you have to suppress on site security and gain access to a bunker designed to keep people like you out) inside the bunker and have access to some of the Lance missile warheads (assuming you have prevented the guards from disabling them). You can't detonate them as that requires either access to the PAL code or the time and expertise necessary to remove them (tactical weapons had PAL according to these two links
http://www.usarmygermany.com/Sont.h...any.com/units/ordnance/USAREUR_59thOrdBde.htm
http://cryptome.org/nuke-fuze.htm).
You don't have time because whats left of site security and everyone at Giessen who can carry a rifle is going to be fighting like devils to at least hold you in place and hopefully retake Site 4.
The QRF is inbound (elements of the 3rd Armored division) bringing MBTs, APCs, infantry and probably indirect fire and attack helicopters and eventually Close air support (given NATO's multinational nature we may see some hot RAF on RAF action

) The RAF is about to get curb stomped, even if they brought along some Spetznaz support (who hopefully have no way of being identified or this incident might have just started WW3)
While you might try and take a warhead with you when you make a break for it (again assuming you can remove them from there storage containers) they are not that small
http://travelphotobase.com/v/USNM/NMQZ115.HTM and you are probably not getting very far.
All in All if you want to heist a nuke, this is not the time or place in history to do so.