Jointly managing water and energy systems, rather than treating each system independently, is recognised as an approach that can lead to a more cost-effective and reliable supply, which is particularly critical in water-rich and developing countries. This has motivated the development of various integrated water-energy simulators, each one catering for specific modelling needs through the use of specific sets of modelling assumptions, e.g., representing water and energy with balance equations, or dedicated river flow and power network equations. In this context, it becomes critical to assess the effectiveness of different modelling assumptions to improve the design of water-energy simulators. In particular, it is important to develop a methodology that can identify, based on a systematic assessment process, the portfolios of modelling assumptions that better capture the uncertain future conditions in the water and energy sectors, e.g., climate-driven stresses and shocks such as water scarcity, temperature rise, etc. To address this challenge, this paper proposes a Mixed Integer Linear Programming (MILP) integrated water-energy system simulation methodology designed to adapt and quantify different modelling assumptions under various weather-related conditions (e.g., water scarcity and high temperatures). The models were developed to capture the characteristics of non-pressurised water systems (e.g., channels and rivers) and electricity systems. The methodology is used to investigate typical modelling assumptions (e.g., temporal resolutions and water and power system models) and novel approaches to model the impacts of high temperatures on generation capacity to capture the effects of extreme weather on power generation. The methodology is demonstrated on the Ghanaian integrated water-energy system. The results highlight the benefits in terms of computational costs and modelling accuracy, of the customisable simulation, and provide guidance to select adequate modelling assumptions.