Looking for Advice on Cold Emailing in a tight-knit banking community

I'm currently working as a 1st year Valuation Analyst in a smaller Northeastern city. While I am certainly getting some good experience from this role, I know I want to lateral into IB and I think now would be the best time for me to leverage my current skills into a move (especially so I don't get entrenched).

To this end, I've been slowly reaching out to boutiques and MM banks in this area, through cold emailing and LinkedIn. I'm early in the process right now, but I'd say I've had moderate success. There is one boutique firm where I have an alumni contact high up at the MD position. The issue here is one of the Directors I work with at my boutique Valuation firm, used to be a colleague of this MD, and I'm afraid this might lead to a potential conflict of interest. While I know the MD has no reason to contact my Director and tell them I reached out to them, it's quite possible that they did have a good relationship. I don't want to ruffle any feathers at my current firm while attempting to make this move. But then again, the MD might not bother, or even think, to go out of his way and let his old colleague know about my reaching out.

I feel like I'm overthinking this, but what are your guys' opinions?