Building on the earlier suggestion, you might want to look into a grip extension or a dedicated cage setup to balance out the weight if you decide to go with a V-mount later. Since you have a wedding coming up fast, honestly just keep it simple so you dont have to troubleshoot gear while the bride is walking down the aisle. Here are a few ways to handle the power situation without just buying a pile of expensive OEM packs:

• The SmallRig NP-FZ100 Dummy Battery 4232 is a solid middle ground. Pairing this with a decent PD bank like the Anker PowerCore 737 24000mAh 140W gives you hours of runtime. Just make sure the bank supports 9V/3A output or it wont keep up with 4K video.
• If you prefer a cleaner look, the Kondor Blue D-Tap to Sony NP-FZ100 Power Cable is way more reliable than the cheap stuff on Amazon. It connects to V-mount plates, which is the pro standard for a reason. Look, the overheating stuff is usually about airflow. If you keep the screen flipped out and away from the body, you get better heat dissipation. V-mounts add weight but they also act as a counterbalance if you have a heavy lens on the front. Dont overcomplicate it this close to the date, just test your chosen setup at home for an hour straight before you leave.

Honestly, stick to the native batteries for a wedding. Its way too risky to mess with dummy batteries when youve got one shot at the ceremony. I always grab a few extra Sony NP-FZ100 Z-series Rechargeable Battery packs. They are pricey but they just work every single time without overheating the internal boards. If you really need external power for long shots, be careful with random power banks. I use the Anker PowerCore 737 Power Bank 24000mAh 140W because it supports the PD output that the camera actually likes. Just dont try to rig up a bulky V-mount if you're handheld, that will kill your wrists by the reception. Keep it simple, buy two more native batteries, and keep them in your pocket. Reliability is everything when you are on the clock.

Jumping in here because I've shot plenty of weddings with the A7IV and video really kills those cells. If you want to avoid the bulk of a V-mount but need more juice, look into the SmallRig NP-FZ100 Dummy Battery Adapter Kit. I've used this specific setup with a Anker PowerCore 737 Power Bank 24000mAh for years and the USB-C PD delivery is rock solid. Just make sure the power bank outputs at least 30W or higher to prevent the camera from pulling from the internal battery. Honestly, the overheating myth is usually caused by people using cheap, unregulated dummy adapters that spike voltage. As long as you use a quality PD-compatible bank, the camera manages heat fine because you arent dealing with the constant chemical charging cycle. Itll definitely be lighter than a full cage rig.