I suspect your issue is the proverbial "(coaxial) tail wagging the (breadboard) dog".
Step 1. Firmly secure the board and coax within a few cm of each other to your bench. ( or as close as convenient)
Step 2. Use a bulkhead jack on the coax and solder to it with a twisted pair of solid AWG 20 hookup wire. Tape down anything loose.
It depends on your expectations for presentation, fit and function. Most student labs have BNC to banana jacks and some breadboards have banana jacks. Then using a twisted pair of AWG 20 you can make a neat connection if try to avoid loops that may act as antenna for AM signals in high Z Rx circuits. Your idea will work, but some EE's might cringe at the sight of alligator clips.
Marine Band uses 40m band (7MHz) and ships might use a 7m stiff antenna with a 1 kW HF transmitter. I suspect you are not doing this. ;) nor using VHF. 30~300 MHz)
Modern breadboards include a solid ground plane that helps shunt crosstalk to ground.
I estimate parasitics about 0.6 pF /cm for twisted pairs and about 8 nH/cm for Effective Series Inductance (ESL) for ~ 120 ohm wire pairs ( a bit less C for adjacent touching wires) Zo = √(L/C)
If your circuit can tolerate a couple of pF crosstalk at 7 MHz just beware that parasitic positive feedback must be less than negative in a high GBW Op Amp. That is why Vin- is next to Vout.
Using your finger to poke around short wires and to keep them neat and close to the board while viewing any critical signals will tell you if your layout is too sensitive. The scope-probe earth ground to your signal 0V should be short (ESL) and ought to remove all e-field line noise. You may also use the scope's 20 MHz LPF.