Designing binders to target undruggable proteins presents a formidable challenge in drug discovery, requiring innovative approaches to overcome the lack of putative binding sites. Recently, generative models have been trained to design binding proteins via three-dimensional structures of target proteins, but as a result, struggle to design binders to disordered or conformationally unstable targets. In this work, we provide a generalizable algorithmic framework to design short, target-binding linear peptides, requiring only the amino acid sequence of the target protein. To do this, we propose a process to generate naturalistic peptide candidates through Gaussian perturbation of the peptidic latent space of the ESM-2 protein language model, and subsequently screen these novel linear sequences for target-selective interaction activity via a CLIP-based contrastive learning architecture. By integrating these generative and discriminative steps, we create a Peptide Prioritization via CLIP (PepPrCLIP) pipeline and validate highly-ranked, target-specific peptides experimentally, both as inhibitory peptides and as fusions to E3 ubiquitin ligase domains, demonstrating functionally potent binding and degradation of conformationally diverse protein targets in vitro. Overall, our design strategy provides a modular toolkit for designing short binding linear peptides to any target protein without the reliance on stable and ordered tertiary structure, enabling generation of programmable modulators to undruggable and disordered proteins such as transcription factors and fusion oncoproteins.