The new forum software is much easier to do something like this.
Edit post
Backspace over or DEL to delete existing broken image in the post to remove it
Copy the image URL of the replacement image on your new hosting site (i.e. not photobucket)
Paste the image URL of the replacement image into the post at the cursor location (e.g.http://www.somephotosite/wrenneire/murphyalbum/IMG1234.jpg )
The new forum software will automatically convert the new URL into a visible image which will appear before your eyes within a second or two.
Repeat if any other images in the post.
Save the post
A few hours should do it. With the old vBulletin BB it only took me a few hours to update all my old posts with images. What will take you time is to re-upload the images to your new photo hosting site (assuming you still have the original JPGs), or alternatively you can still download each of your PhotoBucket albums one at a time to your PC and this saves you downloading images one at a time (e.g. if you download a PB album with 200 images, all 200 will download to your PC in one step). You may then be able to use a bulk upload tool with your alternate image hosting web site.
IMHO, that superb Lima Murphy Models thread is worth the effort if you have the time.
PS: It looks like the new forum has a photo storage cache, so copies of linked images are stored here and therefore will never be lost again in the future (i.e. insulation against typical issues like albums being moved, renamed or deleted, photobucket, dropbox policy changes, etc). A good idea thanks to Stephen.