Hair artifacts in dermoscopic images present significant challenges for accurate skin lesion analysis, potentially obscuring critical diagnostic features in dermatological assessments. This work introduces a fine-tuned SegFormer model augmented with dropout regularization to achieve precise hair mask segmentation. The proposed SegformerWithDropout architecture leverages the MiT-B2 encoder, pretrained on ImageNet, with an in-channel count of 3 and 2 output classes, incorporating a dropout probability of 0.3 in the segmentation head to prevent overfitting. Training is conducted on a specialized dataset of 500 dermoscopic skin lesion images with fine-grained hair mask annotations, employing 10-fold cross-validation, AdamW optimization with a learning rate of 0.001, and cross-entropy loss. Early stopping is applied based on validation loss, with a patience of 3 epochs and a maximum of 20 epochs per fold. Performance is evaluated using a comprehensive suite of metrics, including Intersection over Union (IoU), Dice coefficient, Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index (SSIM), and Learned Perceptual Image Patch Similarity (LPIPS). Experimental results from the cross-validation demonstrate robust performance, with average Dice coefficients reaching approximately 0.96 and IoU values of 0.93, alongside favorable PSNR (around 34 dB), SSIM (0.97), and low LPIPS (0.06), highlighting the model's effectiveness in accurate hair artifact segmentation and its potential to enhance preprocessing for downstream skin cancer detection tasks.