Shortening a frame by cutting and re-welding will not decrease the strength of the frame if the fabrication and welding is done correctly.

If fish plates and boxing plates are used it will actually make the frame stronger at the area of the modification.

Some fish plate examples:

http://i645.photobucket.com/albums/...0Truck%20Stuff/237150184_zpsf29200f5.jpg

http://i645.photobucket.com/albums/...t%20Truck%20Stuff/images_zps471e5763.jpg

http://i645.photobucket.com/albums/...uff/gallery_1277_6_97331_zpsb711cc29.jpg

http://i645.photobucket.com/albums/...0_0_100_100_gsframe64600_zps1192ba4b.jpg

Boxing plate layout (used this on my '27 Roadster Pickup):

http://i645.photobucket.com/albums/uu176/lakeroadster/1927%20Ford%20RPU/Untitled_zps1ef78597.jpg

http://i645.photobucket.com/albums/uu176/lakeroadster/1927%20Ford%20RPU/200305DSCF0030.jpg