Most methanotrophs are proteobacteria, and there are reports of proteobacteria successfully electroporated / electrotransformed either in pure water (e.g. E. coli as reported in Calvin NM, Hanawalt PC. High-efficiency transformation of bacterial cells by electroporation. J. Bacteriol. 170: 2796–2801, 1988 ), or - if your particular bacterium cannot take such hypoosmolarity - in ~270 mM sucrose (e.g. various sp. of Yersinia as reported in Conchas RF, Carniel E. A highly efficient electroporation system for transformation of Yersinia. Gene 87: 133–137, 1990 ).
Perhaps neither will work for your particular bacterium, but I guess it would be simple and thus worth to try.
Instead of sucrose, also glucose and maltose are often used to achieve the desired osmolarity without increasing the medium's electrical conductivity and thus current and heating.