you said you have a 4.5 space take the wood and put a 1/2" thick x 4" wide, steel plate on or in the middle of the wood, bolt ii together, and put in the header, the header will be 3.5" wide
if you want steel only used a 4" deep by 3" wide, steel tube, 3/16 wall, and go for it, If still concerned go with 1/4 wall, I do not have any chart but I know it would more than hold the load, the construction and load proprieties of the floor and other are normal.
you do not say the floor load, and width of the floor that is to be bearing on this header, or if there is a wall above it or how it is constructed, (even the floor joists depth), as been stated, one could put the header use the space the joists take up and put some joist hangers on the header to hold the floor joist in the header area, (even if the floor joist were 2x6, and you say you have 4.5" that is 10" of space for a header, and If my recall is correct a 2x10 is only 9.25" wide, add a one by on top of the header to match the top of the joists and put down ply wood sub flooring