Open sourced doesn`t to 100% safety and doesn`t mean it must be more secure than a wallet that not open-sourced. Because open source means that more people can act as monitors to ur code, but also gives ppl chance to figure out the mistake in your code.
Open source doesn't guarantee to have less security flaws.. but it doesn't need any trust into the developer anymore.
Anyone is free to investigate the source code. Verify, don't trust.
I wouldn't say that an open source software gives an opportunity to a malicious person. Security by obscurity is - and always was - a bad idea.
If you have vulnerabilities in your code, they will be found. Doesn't matter whether open source or not.
But, with open source you may have some good guy find the vulnerability.. in a closed source project you are almost guaranteed that the vulnerability is being found by a malicious person.
Also, a wallet that recommends by Bitcoin.org
Honestly, this alone shouldn't be a reason to
trust a wallet software.
It's not necessary in bither's case anyway, but worth to be mentioned.
@OP
I would recommend mycelium. I am using it quite often and have nothing to complain about.