You most definitely do not have to weld aluminum to get a strong outcome. It is easily cut and drilled and is light and super rigid .... IF you use the right material. You won't find the correct alloy at Home Depot. They only carry the dead soft stuff which is useless for any structural project. A metal supply company that specializes in non-ferrous metals (no regular steel) will have what you need, or you can order online.
My suggestion is this:
Buy some lengths of 6061-T6 (tempered) aluminum channel; this size would work fine:
http://www.alcobrametals.com/display.php?id=523
Cut to length to make four full height risers, and bolt them to the sides and bottom structure of your trailer using several 1/4-20 or larger bolts and self locking (Nylock) nuts. You want the vertical load to be carried by the steel trailer frame, not the wood sides.
Then make four short sections (2"x2") and bolt them to the top of the risers to make horizontal pads. Use a u-bolt (two is better, but probably overkill for your load) at each end of a crossbar to form your load bars. I recommend the Yakima plastic coated steel bars - they are strong as can be and won't rust, and you can use standard Yak mounts and accessories. You could even mount a kayak rack up there
or just wrap them in dense foam. If your bike racks are Thule, you can use their rectangular bars, but they are a little harder to work with IMHO, and less versatile.
FYI here is a list of common aluminum alloys: ....
http://www.alcobrametals.com/guide.php?metal=1#6061
The reason you use channel instead of angle is that it resists twisting so much better. Angle easily distorts under modest loads, so you have to increase the thickness to get enough strength, and that adds weight and cost.
BTW, that place I linked is very close to me and I buy stuff all the time, especially since I have an aluminum trailer; they do mail order, but shipping costs may be an issue. So a local supplier is probably better. Any major metro area should have one.
Here is a pic of Yakima bars mounted with stainless u-bolts on my trailer lid. It is hell for strong and a simple setup. The Space Booster and Boa bike mounts go on and off in just a few minutes.
Good luck.
EDIT: Oh yeah - any aluminum scraps you have left when you are done can be recycled for cash and you will get a little of your money back.
John Davies
Spokane WA USA