No, no no trouble,
The relay, all be it a bit low for your voltage, the coil is rated again at 5V 70 -71 mA, and at again 9v it allows 127 agv mA, the coil can get rather warm with this,
to get the IC to drive that relay, the IC would have to be the power sender, meaning the pin 3 becomes the positive supply.
Pin 3 would need to be the relays positive, then the other end of the coil directly to the common GND to power supply, however the flyback diode now needs to be placed at the pin 3 to relay point then directly to the power supply positive.
Recap. 555IC pin 3 to relays chosen positive, relays chosen negative to main power common, flyback diode annode to the pin 3 relay connection, Cathode to the main supply positive.