Late in on this:

a) The only way a relay could affect fan noise would be if it is chattering - thereby causing the fan to chatter. Brush-type DC motors are generally not fond of low-frequency intermittent voltage.

b) And, if an automotive relay is in any way questionable - replace it outright. The alternative might be a 3:00 am breakdown during a blinding snowstorm. To this end, I know a number of individuals (including me) that carry spare relays for critical functions when on road-trips or off the beaten path. And, I know where those of that nature live in both vehicles.

There is frugal - spending money wisely.
There is parsimonious - which is frugality taken to the extreme.
There is being miserly - which has high potential for negative consequences..

Be frugal, and/but try not to be stupid about it.

My road-trip "Spares Kit" includes: Fuel Pump, Headlight, and Main Systems relays. High and Low beam, turn-signal and brake lamps, if applicable. Fuses. Black electricians tape. Good gloves. Very, very good Jumper cables. Flat-fix x 2. Canvas tarp.

Come to kindly terms with your Ass, for it bears you - John Muir.

Peter Wieck
Melrose Park, PA