Deploying Small Language Models (SLMs) on edge devices requires efficient fine-tuning strategies that adapt models to new tasks without degrading their general capabilities. In this study, we benchmark five sub-1B models (135M-1B) on mathematical reasoning tasks and uncover a critical vulnerability: Full Fine-Tuning (Full FT) actively harms performance in models under 300M parameters, often dropping accuracy below zero-shot baselines. This "negative transfer" makes Parameter-Efficient Fine-Tuning (PEFT) not just an efficiency preference, but a stability requirement. We find that while Low-Rank Adaptation (LoRA) and Weight-Decomposed LoRA (DoRA) perform comparably, their strengths vary by task; DoRA excels in complex reasoning (GSM8K), while LoRA dominates pattern matching (OrcaMath). In particular, Full FT is outperformed by LoRA on aligned models (Qwen2.5-0.5B) and even by simple 5-shot In-Context Learning on the smallest architectures (SmolLM2-135M). Based on these findings, we recommend defaulting to PEFT for all aligned sub-1B models and caution against Full FT for any architecture smaller than 500M parameters to prevent catastrophic forgetting. Reproduction of this work can be found at https://github.com/gulguluu/tiny-slm-finetune-compare.