No, it would be very unusual for melting glaciers to produce methane. Methane comes from the melting of permafrost which is organic soil and tends to form in flat low altitude high latitude regions. Glaciers do not contain organic matter and those in Nepal are in a steep high altitude low latitude region, so they will not produce methane.
First you need to say which definition of 'climate change' you refer to. There are three different versions in common usage;
1) Dictionary.com;
“A long-term change in the Earth’s climate.” (Dictionary.com 2017)
2) UNFCCC;
"Climate change" means a change of climate which is attributed directly or indirectly to human activity that alters the composition of the global atmosphere and which is in addition to natural climate variability observed over comparable time periods.” (UNFCCC, 1992)
3) IPCC in AR4;
“Climate change in IPCC usage refers to a change in the state of the climate that can be identified (e.g. using statistical tests) by changes in the mean and/or the variability of its properties, and that persists for an extended period, typically decades or longer. It refers to any change in climate over time, whether due to natural variability or as a result of human activity.”(Solomon, 2007)
Robert Holmes Regardless of the definitions for climate change, glaciers are decreasing in size due to that we raised the global temperature by releasing greenhouse gases (GHG). We are fortunate that glaciers do not contain trapped methane. Permafrost in the soils below the glaciers certainly contain methane which is a serious concern that we might get more GHG into the atmosphere.
the current methane concentration, and its annual growth rate to calculate the global methane emission rate. The up-per and lower limits of the annual global methane emission rate, depending on loss of CH4 into the stratosphere and methane consuming bacteria, amounts to 648.0 Mt a−1 and 608.0 Mt a−1. These values are in reasonable agreement with satellite and with much more accurate in situ measurements of methane. We estimate a mean tropospheric and mass-weighted temperature related to the reaction rate and em-ploy a mean OH-concentration to calculate a mean methane lifetime. The estimated atmospheric lifetime of methane
amounts to 8.28 years and 8.84 years, respectively. In order to improve the analysis a realistic 3D-calculations should be performed.