I am trying to transfer my photos from macbook to mac mini, can i do this without a cord?

You can use Airdrop between your Mac Mini and your MacBook. This involves ensuring that Airdrop is enabled on both devices.

I have often moved photos or folders between my iMac or iPhone and my MacBook Air. It's a good idea to establish whether your Mac Mini is supported for Airdrop:

AirDrop won't work on all Macs and all iOS devices, so it may not be a feature you can take advantage of. AirDrop is (apparently) supported by the following Mac models: MacBook Pro (Late 2008) or later, excluding the MacBook Pro (17-inch, Late 2008) ... Mac Mini (Mid 2010) or later.

Then ensure that your wifi is turned on.

How to Activate AirDrop on Your Mac

1. Open “Finder”
2. Select “Go” from the menu bar.
3. Look for “AirDrop.”
4. Wait for an AirDrop window to open.
5. If your Mac's Bluetooth or Wi-fi is turned off, you will be asked to turn them on. ... 
6. In the AirDrop window, you will be asked to choose who you want to see your device.

Whatever photos you wish to Airdrop, you can send en bloc by first highlighting them with the cursor, moving the set of photos to the Airdrop pic that will be shown. Don't try to position them over the Airdrop logo.

This link shows the complete tech specs for every Mac Mini ever made. Click on your model to find out whether your model has AirDrop capability. Otherwise, it could involve the use of a Thunderbolt/Mini Display port cable.

https://everymac.com/systems/apple/mac_mini/index-macmini.html#specs

There are several methods. One is iCloud Photos (be aware it will sync all photos and any future changes, including deletions, in both directions). See: Set up and use iCloud Photos - Apple Support

Another is a 3rd party app: https://www.photosync-app.com/home.html

If you are on a WiFi network, simply enable file sharing on one

or both devices. And simply move files between them in

Finder.