The thermal emission of dust grains is a powerful tool for probing cold, dense regions of molecular gas in the ISM, and so constraining dust properties is key to obtaining accurate measurements of dust mass and temperature. By placing constraints on the dust emissivity spectral index, beta, towards two star-forming infrared dark clouds, SDC18.888 and SDC24.489, we evaluate the role of mass concentration in the associated star-formation activity. We exploit the simultaneous 1.2mm and 2.0mm imaging capability of NIKA on the IRAM 30m telescope to construct maps of beta for both clouds, and by incorporating Herschel observations, we create H2 column density maps with 13 resolution. While we find no significant systematic radial variations around the most massive clumps in either cloud on >0.1 pc scales, their mean beta values are significantly different, with beta = 2.07 +/- 0.09 (rand) +/- 0.25 (syst) for SDC18.888 and beta = 1.71 +/- 0.09 (rand) +/- 0.25 (syst) for SDC24.489. These differences could be a consequence of the very different environments in which both clouds lie, and we suggest that the proximity of SDC18.888 to the W39 HII region may raise beta on scales of 1 pc. We also find that the mass in SDC24.489 is more centrally concentrated and circularly symmetric than in SDC18.888, and is consistent with a scenario in which spherical globally-collapsing clouds concentrate a higher fraction of their mass into a single core than elongated clouds that will more easily fragment, distributing their mass into many cores. We demonstrate that beta variations towards interstellar clouds can be robustly constrained with high-SNR NIKA observations, providing more accurate estimates of their masses. The methods presented here will be applied to the Galactic Star Formation with NIKA2 (GASTON) large programme, extending our analysis to a statistically significant sample of star-forming clouds.