I would like to re-string my tzitzit using a different method. Can I do this? Also, will the strings be irreparably out of shape?
You can unite your strings and then re-tie them with any method of your choosing. The only requirement for reuse is that when retied they will make up a length of 12 thumb-breadths (that is, when the strings were tied, they should not have broken to be less that 12 thumb-breadths).
In order to get the strings straight again so that it will be easier to tie them, I recommend that you soak them briefly in water (enough to get them totally wet) and then let them drip dry over a shower curtain rod (or similar device).