Hedge relay current capacity with additional wiring
You have about 30 mm of wire there. A quick check on a couple of online calculators shows that 30 mm of 24 AWG will have a resistance of about 3 m&Omega;.

From \$ P = I^2R \$ we get power dissipation will be \$ 10^2 \times 0.003 = 300\ \text {mW} \$. I don't think you'll have a problem there. (The 12 V DV version has 160 &Omega; coil which will dissipate 900 mW.)

Voltage drop will be \$ V = IR = 10 \times 0.003 = 30 \ \text {mV} \$.