Just be careful with them because they are stronger than the lip of your bucket which can bend. Rigging a chain from the bottom of the bucket to the top on both sides at the clamps helps. Also if the top edge of the bucket is thin think about welding a full length piece of angle iron one to it to give you some beef to anchor the chains to.
As others posted previously, I would not be concerned about wrecking the clamp-on pallet forks as much as I would be concerned about wrecking the bucket. Again,others gave excellent tips on reinforcing the bucket. With the clamp-on forks, all of the item's weight including the forks weight is being supported by the bottom of the bucket. Definitely reinforce the bucket! From another perspective, keep the forks as close to the ends of the bucket as possible where at least the bucket sides are offering more reinforcement than in the middle of the bucket. A little bit of extra engineering and work was with a friends ingenuity. Right in the middle of his bucket, he sculpted a piece of 1/2' steel plate to match the interior of his bucket, did a continuous weld on both sides of the plate to the bucket. Yes it does somewhat hinder what you are trying to dig/haul with the bucket compartmentalized this way and you have to consider if that might be a concern to you, but now the entire bucket is helping to bear the load of the forks.
I hope that it all works for you successfully and you definitely will find a myriad of uses for those forks. Good Luck - Gary