I'm not so sure. As a whole, yes, global warming is a huge issue, but one shale gas well alone will surely have very marginal effect on that. Comparing that to the fact that it can seriously contaminate groundwater and air in your imminent vicinity seems like a more serious issue in that regard.

A barrel of oil means about 560 kg of co2 emissions. Including the mortality cost til 2100 from emissions bumps the cost of emissions to about $145 per barrel using nrs from[1] (0.56 tons of emissions from a barrel x $260 scc per ton of emissions). I'll leave it to you to quantify the local effects and whether they are worse.

[1] https://pmc.ncbi.nlm.nih.gov/articles/PMC8322393/ - they include effects only to 2100 which is way too short term IMO, should be higher