I think you might be getting a bit ahead of yourself here to be honest!
Firstly, before replacing anything, you need to know what you're working with.
Each soldering station is built to work with a specific heating element (and specific soldering tips, or "bit" if you will)
And secondly, due to the above, replacing the handle with one that uses the wrong heating element will not only not work, but could potentially fry some of the internal components of your station as well! Please be more specific about what soldering station you're using.
Is it a 936 one? And if so, does it use the A1321 or A1322 heating element? If in doubt, you could simply measure the resistance from the connector and figure it out. If it has a 5pin aviation plug, simply measure both pairs marked on this image:
https://s4.postimg.org/816vvo2b1/s_l1000.jpgPut your multimeter on the 200ohm range (if it's not an autoranging one)
Set all that aside, even if the the tip is a bit loose, this by itself shouldn't be an issue.
I too have a 936 clone (with A1322) and while the tip is slightly loose, it heats perfectly fine (I also had it properly calibrated btw)
It's possible that you have a bad heating element, not using the right temperature for the job, or that your station is very poorly calibrated (or it could also be a bad soldering technique!) Personally, I do all my soldering works at 350C, also, I'm not trying to be cocky or anything, but I'm just gonna you two simple pointers that could potentially help you out (depending on your level of soldering experience)
Firstly, when desoldering something, there are two techniques that can be used to properly melt the solder, first one is to apply a bit of flux onto the joint, and then heat it with the iron, second is to apply a bit of fresh solder and then go at it with the iron, if you don't do either of those things (and just try to have a go at an old soldering joint dry, you'll get very poor results!) and also, the size of the soldering tip definitely matters (the bigger/wider it is, the more heat it can transfer) so make sure you use the right kind of tip for the job.