For those who haven't experienced it, going Smiteless is a nightmare at the moment. It's hard to really know how bad it is without actually playing such a game. When going jungle, you already need to be in top form when it comes to runes and masteries; going with support stats could be irritating. However, forgetting Smite is a lot worse.
To begin, you must start the game without your jungle item, and clear camps without a decent heap of damage and sustain. You can maybe make up for the sustain with a Hunter's Potion or regular potions, or maybe the damage, but not both. Once you finish the first camp, you are still level 1, and generally won't hit 2 until after you beat the big monster on the second camp, which likely will not be red/blue buff with your damage. You also can't use the Smite buff from Gromp/Golem, either, as you don't have Smite. If, by some miracle, you had help with the first camp to get a full clear and then had enough to tackle a second camp, you're most likely going to need to back.
Now, Hunter's potion could help, in theory. It is, afterall, a nice, consistent source of sustain, or so it would seem. However, it is meant to sustain very minorly over quick camp clears. With the clearing disadvantage you will find yourself in, the Hunter's Potion really doesn't go a long way. For some comparison, a full Hunter's Potion only heals 2 pots worth (100g worth) at a 400g cost. Each camp you clear gains yet another charge, but that comes in at 60 health per charge, or about 40g worth. Until you find a way to use 20 charges (which will be a few trips back), the Hunter's Potion isn't worth it, and by the time you do get that far, hopefully you've started clearing fast enough that such sustain isn't needed so badly. Honestly, the item's practicality is very debatable in a Smiteless build, despite seeming necessary. If you insist on potions, consider leaving a Refillable potion unupgraded for a cheap fix, or if you really want it, a Corrupting Potion for ganks. Those provide 86g and 113 gold in health on each back, respectively, and the one saves you money while the other gives a small damage edge when ganking.
So, with probably 2 camps out of the way (hopefully one buff), you need to find a way to linger with a very slow clear speed over the rest of your camps. Keep in mind that you are already behind in XP, are never going to catch up to a normal XP rate, and will rarely have a proficient clear pattern. You will generally be 1-3 levels behind (or more) a proficient jungle run, and that is 1-3 levels you are lacking of rune/mastery buffs (for those who still have some per level gains), HP, AD, AS, HP/MP regen, and most importantly, skill levels. Those are also stats you would try to use on a gank, if you are feeling gutsy, and sometimes it means utility you lack for ganking because you have to invest so heavily in your damage abilities. Lastly, this slow leveling pattern is best case scenario, assuming limited jungle ganks or pressure, as well. And I am not going to go into the team morale side of things, as OP implied...
It really is just a nightmare.