Or maybe the question should be, "Can I just switch the strings around on a fiddle to make it left-handed"? The answer to that question is no, and there are some very good reasons why:
Interior Construction - Every fiddle has a bass bar that is part of the internal construction of the top of the instrument. On some cheaper instruments, the bass bar is actually carved into the top of the fiddle. All good quality instruments (and even most student quality instruments) have a bass bar that is a separate piece of wood that is fitted to the top of the fiddle and glued in place. The bass bar provides strength to the top of the instrument, and it also helps bring out a good, low end (tone quality) to the instrument. The bass bar is on the side of the fiddle that has the low strings on it (G & D). If you switch the strings around, the strength provided to the top of the instrument will be on the wrong side, and this will also negatively affect the tone quality of the instrument. Both of these things could be ignored and, as a general rule, would not cause the fiddle any physical harm to the instrument.
The sound post is a major factor in how a fiddle sounds when it is played. This is the little stick of wood that looks like a dowel rod on the E string side of the inside of the fiddle. It is not glued into place, but is positioned with a special tool to sit right behind the bridge opposite the bass bar. You can't change the positioning of either the bass bar or the soundpost without changing the positioning of the other, and since the bass bar is glued into place, this would not be an easy (or economical) thing to change.
(Click on the picture to make it larger)
Angle of the Fingerboard - The neck and fingerboard of a fiddle should be tilted slightly towards the E string side of the instrument. This angle (tilt) creates a better bow arm position and less bow arm fatigue. Can you get used to it differently? Yes, in theory you could.
In this picture, I actually took two pictures, one of each side of the same fiddle, and then pasted them facing each other so you can see how the E-string side of the neck is slightly smaller (lower) than the G-string side.
(Click on the picture to make it larger.)
The next picture shows how the E-string side of the fingerboard is lower (closer) to the top than the G-string side.
(Click on the picture to make it larger.)
Positioning of the Pegs - A true, left-handed fiddle will have the pegs drilled opposite. Changing the strings around without refitting the pegs may cause several different issues. For one, the peg closest to the fingerboard may interfere with hand position. (This depends upon how large your hands are and the exact positioning of your hand on the neck of the fiddle.) The second issue is the angle of the strings coming off the pegs and going across the nut. Strings may rub on other pegs in the pegbox, or the angle could cause premature string breakage at the peg or nut. Since the pegs are fitted on a taper, you cannot just switch them around. The peg holes have to be bushed (filled in and redrilled).
So why am I telling you all this? Because many unscrupulous sellers (especially on places like E-Bay) will try to sell you a "left-handed" fiddle that is not truly left-handed. Unless you have the correct knowledge, you will not know any better and will end up with something that is hard to play and doesn't sound good.
If you haven't learned to play yet, let me encourage you to learn to play right-handed. Please take the time to read my other blog entry about left-handed people learning to play right-handed:
Left-handed or Right-handed? There is no replacement for a great start!