You theoretically can. You'll need to carefully sand it and use gloves to avoid getting any grease on it. Also
silver solder and probably a torch.
You'll burn the paint...may want to remove it 1st and repaint later. Also don't breath the fumes...get good ventilation. It's not easy...copper is easy to solder. Gold too. Stainless...not so much.
How to Solder Stainless Steel - YouTube
Google "solder stainless steel". The whole thing may be more trouble than it's worth (and I'm broke...so I'm not at all being frivolous with your money when I say that).
Soldering 101 - (quick abbreviated version)
What you do is:
A) Make sure the parts are clean and grease free.
B) Scuffing it up with fine sand paper helps sometimes.
C) you heat the
parts...not the solder. When the parts are hot enough to melt the solder they will form a molecular bond with it.
D) Flux helps the solder flow and helps clean the metals and remove oxides so they bond.
All of this heating assumes it's just the metal involved...no batteries and/or electronics (I think that's the other part in your pic...
not the part you're soldering).
1st thing I'd check .... ask some venders if they sell replacement tubes....