Triplex-forming oligonucleotides (TFOs) are short, single-stranded oligomers that hybridise to a specific sequence of duplex DNA. TFOs can block transcription and thereby inhibit protein production, making them highly appealing in the field of antigene therapeutics. In this work, a primer extension protocol was developed to enzymatically prepare chemical nuclease TFO hybrid constructs, with gene-silencing applications. Click chemistry was employed to generate novel artificial metallo-nuclease (AMN)-dNTPs, which were selectively incorporated into the TFO strand by a DNA polymerase. This purely enzymatic protocol was then extended to facilitate the construction of 5-methylcytosine (5mC) modified TFOs that displayed increased thermal stability. The utility of the enzymatically synthesised di-(2-picolyl)amine (DPA)-TFOs was assessed and compared to a specifically prepared solid-phase synthesis counterpart through gel electrophoresis, quantitative PCR, and Sanger sequencing, which revealed similar recognition and damage properties to target genes. The specificity was then enhanced through coordinated designer intercalators—DPQ and DPPZ—and high-precision DNA cleavage was achieved. To our knowledge, this is the first example of the enzymatic production of an AMN-TFO hybrid and is the largest base modification incorporated using this method. These results indicate how chemical nuclease-TFOs may overcome limitations associated with non-molecularly targeted metallodrugs and open new avenues for artificial gene-editing technology.