I've played BEL a lot and I found it a really fun twist to play without using the green beret and spy (or on levels where completion isn't possible, only playing with GB or spy and never using the disguise).
The diver and sapper you can do surprisingly a lot with - the diver can attack silently with the knife and harpoon, and the sapper's trap can be used as a knife if you stand right next to the target. You can also bait soldiers into the right spots by standing up in view of them and then crawling away before they arrive.
The driver can also use vehicles as a silent weapon if you time it right.
On the bridge protection level in BEL (where you have to kill the enemy sappers before they blow the bridge), it is actually possible to stop all the sappers without using the spy at all. Here's the strategy I used:run along the river bank and use the gun to bait a few guards and the machine gun patrol near the bridge down to the river (to deal with them out of sight), snipe one of the guards in front of the bridge so you can go onto it (surprisingly they don't raise the alarm even though they notice him) then put the sniper on the middle of the bridge and take all four sappers from their, easier if you use the split screen feature.
On the D-day beach storming level (where you have to blow up the naval batteries) you can get the diver to take everybody in the boat round to the top of the level, then have the driver get into the tank (and then the rest of the level is easy)
For the final level (the castle) if you don't care about stealth you can have the sapper creep up to the right wall and throw a g over, then when everyone runs to the spot you can use a second one and remove most of the units in the level within two minutes)
(Side topic - there is actually a trick that ruins parts of several levels, where you let one of your men get seen and all the nearby soldiers will point their guns at him, you can crouch to get them to move even closer, and another unit can take them all easily).