Just like Jaakko stated, pick up a universal charger if it just uses a "wall wart" style charger originally. One thing to be sure of that is not mentioned is to be sure you have the pin connection polarity right. The center pin connection can carry positive or negative DC power while the outer area carries the opposite polarity of the center pin. It should show the polarity on the uk charger. It will look something like this - -C- + . It actually will look like a dot in the middle of a C and show a line coming from that dot to either a + or - and that will be the center pin polarity.
When it comes to the DC current output you should not go over 2C which is equal to 2x the current rating of the cells. If the cells in the pick gun have a current capacity of 2000 mAh then the very highest current they should be charged at is 4000 mAh or 4 amp DC. Your best bet is going to be sticking to a 1C charge rate as that will charge the unit in one hour and be much easier on the cells. The best charge you can get will be at .5C as the cells will charge much cooler and be filled closer to their full capacity rating. Charging at lower C rates will result in longer cell life also. It just depends on what trade offs you want, fast charge or longer cell life. In the above post, C is equal to the capacity rating of the cells which should be printed on the side of the cells. If the gun uses a "C" size nimh cell then their capacity rating should be somewhere between 3000 and 5000 mAh.
You do need to confirm the cell chemistry used. It could be NiCad, nimh, or Li-Ion. If standard Li-Ion cells are used then they will likely be protected cells with either a single cell or a pair of cells wired in parallel configuration which effectively doubles the capacity rating stated on the cells. For example if the cell says Li-Ion 18650 2200 mAh it equates to a cell 18mm in dia, 65mm long, and the last 0 in the 18650 number means it is a round cell design. If the gun is designed around a Li-Ion cell then you need to get a UK to US plug adapter assembly and use the factory charger or buy a GOOD dedicated Li-Ion charger that offers the ability to balance charge the cells if the plug connection on your pick gun is set up right for balance charging. You will likely either have to call customer support to determine if they are balance charged or disassemble the gun and examine the wiring configuration. Li-Ion cells should always be charged with alot of caution and never substitute a standard NiCad/nimh charger as it will not charge at the right voltage nor will it sense the full charge signal from the cell. It is also possible that a newer Lithium type rechargeable cell is used such as an Emoli cell etc. There again you need a charger rated to charge emoli cells. A good Li-Ion, emoli, etc type charger is going to run you atleast $75 for a balancing charger. On the topic of chargers, if you determine that it uses NiCad cells or nimh cells you can buy a much cheaper charger but it must be rated for the cell chemistry type (nimh or NiCad). There are decent chargers out there that are cheap that are compatible with both nimh and NiCad. But you cannot use a NiCad only charger on nimh or vise versa due to the sensitivity difference of the chargers to register a fully charged cell. If you use the wrong charger it will either not fully charge the cells or severely overcharge the cells and ruin them.
I know that is a long winded post but caution must always be used on standard rechargeable Li-Ion cells especially if they are an unprotected type. It should state on the cell shrink wrap whether it is protected or not. If it doesn't then it should be assumed that the cell is unprotected and in this case you should always be present when the cells are being charged as you can end up with a pretty violent cell explosion or a cell fire that is just like all of the dell laptop batteries a while back which was due to a faulty charger or faulty charging logic on the laptop psu board. The newer chemistry Li-Ion type cells such as emoli's are a much safer chemistry all around.
Just be sure you know what you're dealing with before plugging the thing in the wall
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